Common Course Numbers, Titles, Rationale, Content

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1 Common Course Numbers, Titles, Rationale, Content Document last updated on 09/12/2014. PLEASE report any additions, deletions, or other changes to your college s Math Issues representative. Course Number MAT* Course Title Comments 287 Set Theory and Foundations 2 8 _, 2 7 _, and 2 6 _ 285 Differential Equations : Courses with a minimum of Calculus II 272 Linear Algebra 268 Calculus III: Multivariable 256 Calculus II 2 5 _ and 2 4 _: Calculus 254 Calculus I I and II 250 Calculus I with Lab 243 Projects in Calculus II 242 Projects in Calculus I Applied Calculus Applied Calculus with Modeling 2 3 _: Applied Calculus/Business Calculus and Discrete Mathematics courses with a minimum of one course beyond the Intermediate Algebra level 222 Statistics II w. Technology Apps 2 2 _: Second level courses in Statistics 210 Discrete Math 201 Statistics 191 Calculus - Business/Soc Sci II 1 9 _ : Calculus courses 190 Calculus - Business/Soc Sci I with Intermediate Algebra 187 Precalculus Mathematics 1 8 _ and 1 7 _ : 186 Precalculus Precalculus, Trigonometry,

2 185 Trigonometric Functions College Algebra with 181 Right Triangle Trigonometry Trigonometry, and College Algebra courses with 175 College Algebra & Trigonometry Intermediate Algebra 173 College Algebra w/ Technology 172 College Algebra 170 Math Education in Practice 169 Elem Stat & Probability II 1 6 _ : Statistics courses 168 Elem Stat & Probability I with Intermediate Algebra 167 Principles of Statistics ## 165 Elem Stats with Computer Apps 158 Functions, Graphs and Matrices 1 5 _ and 1 4 _ : Courses, 155 Technical Mathematics II not belonging to 1 9 _, 1 8 _, 1 7 _, or 1 6 _ categories, with 154 Technical Mathematics I Intermediate Algebra 152 Finite Mathematics 151 Financial Math 149 Structure of Math - Geometry 148 Geometry 147 Mathematics for Elementary Teachers II 146 Math for the Liberal Arts 145 Math for Elementary Teachers I 144 Math for Elementary Ed: Geometry, Data 143 Math for Elementary Ed: Algebra, Number Systems 142 Math for the Natural Sciences 141 Number Systems 139 Elementary and Intermediate Algebra Combined 1 3 _ : Algebra and Topics 138 Intermediate Algebra w/ Modeling courses with Elementary Algebra 137 Intermediate Algebra 136 Intermediate Algebra 135 Topics in Contemporary Math 127 Elementary Statistics w/ Technology 1 2 _ : Statistics and 124 Elementary Statistics II Applied Mathematics courses with 123 Elementary Statistics Elementary Algebra 122 Statway II 121 Apps for Business, Other Careers 117 Introduction to Finite Math 1 1 _: Courses, not

3 115 Math for Science & Technology belonging to 1 3 _ or 1 2 _ categories, with Elementary Algebra 109 Quantitative Literacy 1 0 _: Courses with 106 Fundamentals of Algebra II Elementary Algebra 104 Quantitative Reasoning 103 Mathematics of Finance 097 Elementary Algebra Foundations w/ Prealgebra 0 : Foundations courses 096 Algebra, Num Sens&Geom Concept with no mathematics credit 095 Elementary Algebra Foundations 094 Introductory Algebra 093 Introductory Algebra 092 Statway I 085 Pre-Algebra & Elem Algebra 075 Prealgebra: Number Sense, Geometry 073 Prealgebra: Number Sense One objective of the Math Issues Committee, which is responsible for Common Numbering, is to generate a list of common topics among the mathematics courses in the community college system. The committee defined its review process as follows: 1. Courses (other than Calculus I and Calculus II) can be considered equivalent if 80% of the content is the same; 100% compliance is necessary on the Calculus I and Calculus II topics. 2. Committee representatives will identify a list of common topics for each course. This list is to be shared with our respective college departments. Any concerns, recommended additions, or recommended deletions will be brought to the next meeting. 3. After discussion and consensus, the list of common topics along with the corresponding course numbers and names can be documented for articulation reference. 4. Transferring students should obtain a copy of the appropriate syllabus to determine if there are content/ approach differences that the student should address so as not to be at a disadvantage. Differential Equations topics: 1. Basic concepts (classification, solutions, etc.) 2. First-order differential equations 3. Second-order linear solutions 4. Higher-order linear equations with constant coefficients 5. Laplace transformation 6. Systems of linear first-order equations 7. Numerical methods 8. Applications Calculus III topics: 1. Parametric equations

4 2. Polar coordinates * (may be offered in Calculus II) 3. Vectors - dot and cross products and applications 4. Vector-valued functions and applications 5. Functions of several variables - limits and applications 6. Partial differentiation and applications 7. Multiple integration and applications 8. Vector calculus Calculus II topics: 1. Antiderivatives and applications of the integral 2. Transcendental functions and their inverses 3. Derivatives and integrals of transcendental functions and their inverses 4. Techniques of integration 5. Numerical methods 6. Indeterminate forms and L'Hopital's Rule 7. Improper integrals 8. Sequences and infinite series 9. Polar coordinates * (may be offered in Calculus III) Calculus I topics: 1. Limits and continuity 2. Derivatives 3. Techniques of differentiation 4. Applications of differentiation 5. Antiderivatives 6. Fundamental Theorem of Calculus and the definite integral 7. Applications of the integral Applied Calculus/Calculus for Business and Social Sciences* topics: 1. Function review 2. Limits and continuity 3. The derivative 4. Techniques of differentiation 5. Optimization problems 6. Exponential and logarithmic functions and their derivatives 7. Antiderivatives and the Fundamental Theorem of Calculus 8. Techniques of integration 9. Applications *While the mathematics concepts in these courses are approximately equivalent, the nature of the applications differs significantly. Precalculus topics: 1. Concepts of functions 2. Numeric, algebraic, and graphic techniques as applied to the following functions: polynomial, radical, rational, exponential, logarithmic, and circular/trigonometric 3. Right triangle trigonometry and applications 4. Trigonometric identities and equations 5. Modeling and applications

5 6. Topics in analytic geometry Trigonometry topics (2 or 3 credit course) 1. Circular functions 2. Numeric, algebraic, and graphic techniques as applied to trigonometric functions 3. Right triangle trigonometry and applications 4. Trigonometric identities and equations 5. Inverse trigonometric functions 6. Oblique trigonometry and vectors College Algebra Topics 1. Concepts of functions 2. Numeric, algebraic, and graphic techniques as applied to the following functions: polynomial, piecewise, rational, radical, exponential, logarithmic 3. Complex numbers 4. Modeling and applications 5. Systems of Equations Following are some additional topics that may be included: Recursively defined functions Topics in Analytic Geometry Statistics topics: 1. Concept of population and sample, basic experimental designs, introduction to data collection methods 2. Organizing and describing data with (a) graphical techniques (b) numerical methods (calculating statistics and giving meaning to them) 3. Basic probability theory 4. Discrete and continuous probability distributions 5. Normal curves and applications 6. Making inferences about populations (a) point estimates (b) interval estimates (c) hypothesis tests 7. Relationships between two variables (a) scatterplots (b) correlation (c) regression ## NOTE: A statistics course with technology assumes a department philosophy that a significant aspect of the course applies platformed-based software or uses the very considerable statistical features of an appropriate graphing calculator. It is expected that the technology use will be regular and considerable Liberal Arts Course Statement of Principle: Because of the diversity of student needs in a Liberal Arts course, there is no one course that all students take. Thus, an appropriate approach is to describe philosophy rather than content. The following quotes from the American Mathematical Association of Two-Year Colleges publication Crossroads present an accurate Statement of Principle. Concerning pedagogy from page 42: Every college graduate should be able to analyze, discuss, and use quantitative information; to develop a reasonable level of facility in mathematical problem solving; to understand connections between mathematics and other disciplines; and to use these skills as an adequate base of life-long learning" (MAA,1993, p.8). Keith and Leitzel (1994) suggest "more student interaction, problem-solving and understandable application" (p.6) as a productive approach for producing quantitatively literate graduates. Regarding content from page 41: The goals of the course are to develop, as fully as possible, the mathematical and quantitative capabilities of the students; to enable them to understand a variety of applications of mathematics; to prepare them to think logically in subsequent courses and situations in which mathematics occurs; and to increase their confidence in their ability to reason mathematically. Intermediate Algebra topics: 1. Functions, relations, and graphs

6 2. Modeling and applications 3. Linear functions and inequalities 4. Quadratics and other polynomial functions 5. Exponential functions and radical expressions 6. Rational expressions and equations 7. Quadratic equations and applications Elementary Algebra topics: 1. Signed numbers and applications 2. Real number system and properties 3. Linear equations and inequalities - solutions, models, and applications 4. Graphing linear equations - slope and intercepts 5. Polynomials - addition, subtraction, multiplication, factoring 6. Integral exponents and laws of exponents 7. Roots 8. Systems of equations Following are some additional topics that may be included: Graphing nonlinear relations Rational expressions Radical expressions Prealgebra Topics: 1. Whole numbers: concepts, operations, and applications 2. Fractions and decimals: concepts, operations, and applications 3. Graphs: reading and interpreting a variety of simple graphs 4. Geometry: basic notions and applications 5. Ratio, proportion, percent: concepts and applications 6. Measurement and unit analysis 7. Signed numbers: concepts, operations, and applications 8. Transition to algebra: introduction to concept of variables, expressions and equations