Common Course Numbers, Titles, Rationale, Content

      
  
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.

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

1. Parametric equations

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)

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

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.

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

6. Topics in analytic geometry

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

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 Mathematics 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

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. Systems of equations

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. Quadratic equations and applications

          Following are some additional topics that may be included:
          Graphing nonlinear relations
          Rational expressions
          Radical expressions
          Systems of equations

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