College Algebra for Liberal Arts

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1 College Algebra for Liberal Arts C-ID Number MATH 150 Discipline Mathematics Date Approved February 03, 2012 General Course Description College level course in algebra for majors in the Liberal Arts: polynomial, rational, radical, exponential, absolute value, and logarithmic functions; systems of equations; theory of polynomial equations; analytic geometry Minimum Units 3.0 Any rationale or comments Advisories/Recommendations Course Content Functions including linear, polynomial, absolute value, rational, radical, exponential, logarithmic: definitions, evaluation, domain and range; Algebra of functions; Graphs of functions including asymptotic behavior, intercepts, vertices; Equations including rational, linear, absolute value, polynomial, radical, exponential, logarithmic; Linear and nonlinear inequalities; Systems of equations; Complex numbers; and Substantial introduction to at least two of the following: Inverses of functions Transformations of quadratic, absolute value, radical, rational, logarithmic, exponential functions Linear programming Characterization of the zeros of polynomials Matrices and determinants. Properties of conic sections Combinatorics and probability theory Sequences and series Laboratory Activities Course Objectives Upon successful completion of the course, students will be able to: Analyze and investigate properties of functions; Synthesize results from the graphs and/or equations of functions; Solve and apply equations including rational, linear, absolute value, polynomial, exponential, and logarithmic equations; Solve linear and nonlinear systems of equations and inequalities; Apply functions and other algebraic techniques to model real world applications; and For additional topics: Recognize the relationship between functions and their inverses graphically and algebraically Apply transformations to the graphs

2 of functions Use linear programming to solve problems. Apply techniques for finding zeros of polynomials and roots of equations Solve and apply linear systems using matrices and determinants Analyze conics algebraically and graphically Use combinatorial rules to calculate probabilities. Use sequences and series to solve application problems. Prerequisites Intermediate Algebra Corequisites Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level text supporting the learning objectives of this course. Notes

3 College Algebra for STEM C-ID Number MATH 151 Discipline Mathematics Date Approved February 03, 2012 General Course Description College level course in algebra for majors in science, technology, engineering, and mathematics: polynomial, rational, radical, exponential, absolute value, and logarithmic functions; systems of equations; theory of polynomial equations; analytic geometry Minimum Units 4.0 Any rationale or comments Advisories/Recommendations Course Content Functions including linear, polynomial, rational, radical, exponential, absolute value, logarithmic: definitions, evaluation, domain and range; Inverses of functions; Algebra of functions; Graphs of functions including asymptotic behavior, intercepts, vertices; Transformations of quadratic, absolute value, radical, rational, logarithmic, exponential functions; Equations including rational, linear, polynomial, radical, exponential, absolute value, logarithmic; Linear, nonlinear, and absolute value inequalities; Systems of equations and inequalities; Characterization of the zeros of polynomials; Properties and applications of Complex numbers; Properties of conic sections; and Sequences and series. Laboratory Activities Course Objectives Upon successful completion of the course, students will be able to: Analyze and investigate properties of functions; Synthesize results from the graphs and/or equations of functions; Apply transformations to the graphs of functions; Recognize the relationship between functions and their inverses graphically and algebraically; Solve and apply rational, linear, polynomial, radical, absolute value, exponential, and logarithmic equations and solve linear, nonlinear, and absolute value inequalities; Solve systems of equations and inequalities; Apply techniques for finding zeros of polynomials and roots of equations;

4 Apply functions and other algebraic techniques to model real world STEM applications; Analyze conics algebraically and graphically; and Use formulas to find sums of finite and infinite series. Prerequisites Intermediate Algebra Corequisites Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level text designed for science, technology, engineering and math majors, and supporting the learning objectives of this course. Notes

5 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-105 College Algebra Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):4, 3 unit max at CSU. Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 4 Palomar College 4 San Bernardino Valley College 4 One community college in the San Diego area (other than Palomar) 6 at Mira Costa Local Unit Value: 4 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -All of the equivalent courses have more or the same number of units. -Our units match the C-ID minimum. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -4 units provides our students with the same number of contact/lecture hours with faculty. -Although some equivalent CSUs courses provide less credits, they offer contact hours equivalent to 4 units with discussion. -Many of the equivalent CSU courses do not cover as much material as is covered in our course. -Our students in many cases must take the course without access to faculty office hours, which is not the case at any CSU. -Many other CCs offer supplementary workshops for this course while maintaining the same number of units. -Minimum SAT and ACT requirements imply that most UC students already have familiarity with this material, and this course is therefore not offered institution. -Our students will be transferring to a University here they will be competing with students that took the equivalent course with 4 or more units, and possibly more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university.

6 Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago. --80% of community college students begin in developmental coursework. -There are no community colleges that offer less units for the equivalent course. -There are no colleges that offer less classroom time than MSJC. Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used. -C-ID Website -Catalogs for all colleges discussed -Public Policy Institute of California publication Preparing Students for Success in California s Community Colleges by Johnson, H., Mejia, M. and Rodriguez, O.

7 Precalculus C-ID Number MATH 155 Discipline Mathematics Date Approved April 30, 2012 General Course Description Preparation for calculus: polynomial, absolute value, radical, rational, exponential, logarithmic, and trigonometric functions and their graphs; analytic geometry, polar coordinates Minimum Units 4.0 Any rationale or comments Advisories/Recommendations Course Content Functions including linear, polynomial, rational, radical, exponential, absolute value, logarithmic, trigonometric; definitions, evaluation, domain and range; Inverses of functions; Algebra of functions; Graphs of functions including asymptotic behavior, intercepts, and vertices; Transformations of quadratic, absolute value, radical, rational, logarithmic, exponential functions; Equations including rational, linear, radical, polynomial, exponential, trigonometric, logarithmic, and absolute value; Linear, nonlinear, and absolute value inequalities; Systems of equations and inequalities; Characterization of real and complex zeros of polynomials; Unit circle and right triangle trigonometry; Trigonometric and inverse trigonometric identities and formulas; Graphing trigonometric functions: period, amplitude, phase shift, inverse trigonometric functions; and Polar coordinates Laboratory Activities Course Objectives Upon successful completion of the course, students will be able to: Graph functions and relations in rectangular coordinates and polar coordinates; Synthesize results from the graphs and/or equations of functions and relations; Apply transformations to the graphs of functions and relations; Recognize the relationship between functions and their inverses graphically and algebraically; Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, and logarithmic, and solve linear, nonlinear, and absolute value inequalities; Solve systems of equations and inequalities;

8 Apply functions to model real world applications; Identify special triangles and their related angle and side measures; Evaluate the trigonometric function of an angle given in degree and radian measure; Manipulate and simplify a trigonometric expression; Solve trigonometric equations, triangles, and applications; Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs; and Prove trigonometric identities Prerequisites Trigonometry Corequisites Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level text designed for science, technology, engineering and math majors, and supporting the learning objectives of this course. Notes

9 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-110 Pre-Calculus Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):4, 3 unit max at CSU, 3.3 at UCR Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 4 (8 Credits) Palomar College 5 San Bernardino Valley College 4 (8 Credits) One community college in the San Diego area (other than Palomar) 8 at Mira Costa Local Unit Value: 5 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -The equivalent courses at RCCD and SBVC require prerequisite 4 credit trigonometry course, so the students there actually take 8 course units to cover our 5 unit course. -UC mathematics courses include a discussion section, which adds one hour of lecture per week to their course. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -Although equivalent UC course provides less credits, it provides contact hours equivalent to 5 units with discussion. -Our students in many cases must take the course without access to faculty office hours. At UC, students have access to office hours with both a faculty member, and a graduate student. -Many other CCs offer supplementary workshops for this course while maintaining the same number of units. -Minimum SAT and ACT requirements imply that most UC students already have familiarity with this material, and this course is therefore treated as a review at that institution. -Our students will be transferring to a University here they will be competing with students that took the equivalent course with 4 or more units, and possibly more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university. Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago.

10 -80% of community college students begin in developmental coursework. -There are no community colleges that offer less units for the equivalent course. -There are no colleges that offer less classroom time than MSJC. Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used. -C-ID Website -Catalogs for all colleges discussed -Public Policy Institute of California publication Preparing Students for Success in California s Community Colleges by Johnson, H., Mejia, M. and Rodriguez, O.

11 Business Calculus C-ID Number MATH 140 Discipline Mathematics Date Approved December 15, 2012 General Course Description Presents a study of the techniques of calculus with emphasis placed on the application of these concepts to business and management related problems. The applications of derivatives and integrals of functions including polynomials, rational, exponential and logarithmic functions are studied. Minimum Units 3.0 Any rationale or comments Advisories/Recommendations College Algebra for Liberal Arts (C-ID Math 150) or College Algebra for STEM (C-ID Math 151) Course Content Functions and their graphs, including exponential and logarithmic functions; Limits and intuitive limit definition of derivative; Increments, tangent lines, and rate of change; Rules of differentiation including sum, product, quotient, and the chain rule; Implicit differentiation; Applications of differentiation such as marginal analysis, optimization, and curve sketching; Antiderivatives, indefinite and definite integrals; Multiple techniques of integration including substitution; Area between curves; Approximating definite integral as a sum; and Applications of integration in business and economics. Laboratory Activities Course Objectives Upon successful completion of the course, students will be able to: Find the derivatives of polynomial, rational, exponential, and logarithmic functions; Find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule; Sketch the graph of functions using horizontal and vertical asymptotes, intercepts, and first and second derivatives to determine intervals where the function is increasing and decreasing, maximum and minimum values, intervals of concavity and points of inflection; Analyze the marginal cost, profit and revenue when given the appropriate function; Determine maxima and minima in optimization problems using the

12 derivative; Use derivatives to find rates of change and tangent lines; Use calculus to analyze revenue, cost, and profit; Find definite and indefinite integrals by using the general integral formulas, integration by substitution, and other integration techniques; and Use integration in business and economics applications. Prerequisites Intermediate Algebra Corequisites Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level textbook supporting the learning objectives of this course. Notes

13 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-135 Calculus for Social Science and Business Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):3, 3 unit max at CSU, 3.3 at UCR Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 4 Palomar College 4 San Bernardino Valley College NA One community college in the San Diego area (other than Palomar) 4 at Mira Costa Local Unit Value: 4 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -The equivalent course at all the above colleges are offered for the same amount of units -UC mathematics course includes a two hour discussion section, which adds two hours of lecture per week to their course. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -Our students in many cases must take the course without access to faculty office hours. At UC, students have access to office hours with both a faculty member, and a graduate student. -Our students will be transferring to a University here they will be competing with students that took the equivalent course with 4 units, and possibly more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university. Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago. -There are no community colleges that offer less units for the equivalent course. -There are no colleges that offer less classroom time than MSJC. Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used.

14 -C-ID Website -Catalogs for all colleges discussed

15 Introduction to Statistics C-ID Number MATH 110 Discipline Mathematics Date Approved December 15, 2012 General Course Description The use of probability techniques, hypothesis testing, and predictive techniques to facilitate decisionmaking. Topics include descriptive statistics; probability and sampling distributions; statistical inference; correlation and linear regression; analysis of variance, chi-square and t-tests; and application of technology for statistical analysis including the interpretation of the relevance of the statistical findings. Applications using data from a broad range of disciplines. Minimum Units 3.0 Any rationale or comments Typically satisfies general education quantitative reasoning requirement (CSU GE B4). Advisories/Recommendations Course Content Summarizing data graphically and numerically; Descriptive statistics: measurement, measures of central tendency, and variation; Sample spaces and probability; Random variables and expected value; Sampling and sampling distributions; Discrete distributions Binomial; Continuous distributions Normal; The Central Limit Theorem; Estimation and confidence intervals; Hypothesis Testing and inference, including t-tests for one and two populations, and Chi-square test; Correlation, regression lines, and analysis of variance (ANOVA); Applications using data from at least four of the following disciplines: business, economics, social science, psychology, political science, administration of justice, life science, physical science, health science, information technology, and education; and Technology based statistical analysis. Laboratory Activities Course Objectives Upon successful completion of the course, students will be able to: Interpret data displayed in tables and graphically; Apply concepts of sample space and probability; Calculate measures of central tendency and variation for a given data set; Identify the standard methods of obtaining data and identify

16 advantages and disadvantages of each; Calculate the mean and variance of a discrete distribution; Calculate probabilities using normal and t-distributions; Distinguish the difference between sample and population distributions and analyze the role played by the Central Limit Theorem; Construct and interpret confidence intervals; Determine and interpret levels of statistical significance including p- values; Interpret the output of a technology-based statistical analysis; Identify the basic concept of hypothesis testing including Type I and II errors; Formulate hypothesis tests involving samples from one and two populations; Select the appropriate technique for testing a hypothesis and interpret the result; Use regression lines and ANOVA for estimation and inference, and interpret the associated statistics; and Use appropriate statistical techniques to analyze and interpret applications based on data from at least four of the following disciplines: business, economics, social science, psychology, political science, administration of justice, life science, physical science, health science, information technology, and education. Prerequisites Intermediate Algebra or any CSU accepted* statistics pathway curriculum prerequisite*at present there are two mechanisms to become accepted:the proposed statistics course has been accepted to meet CSU General Education Breadth Area B4the pathway has been accepted by the CSU Chancellor's Office process per its October 20, 2015 memo (Statistics Pathways in CSU Quantitative Reasoning) Corequisites Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level text supporting the learning objectives of this course. Notes

17 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-140 Introduction to Statistics Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):3, 3 unit max at CSU, 4 at UCM Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 4 Palomar College 4 San Bernardino Valley College 4 One community college in the San Diego area (other than Palomar) 4 at Mira Costa Local Unit Value: 4 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -The equivalent course at all the above colleges are offered for the same amount of units -UC mathematics course includes a two hour discussion section, which adds two hours of lecture per week to their course. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -Our students in many cases must take the course without access to faculty office hours. At UC, students have access to office hours with both a faculty member, and a graduate student. -Our students will be transferring to a University here they will be competing with students that took the equivalent course with 4 units, and possibly more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university. Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago. -There are no community colleges that offer less units for the equivalent course. -There are no colleges that offer less classroom time than MSJC. Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used.

18 -C-ID Website -Catalogs for all colleges discussed

19 Single Variable Calculus I Late Transcendentals C-ID Number MATH 211 Discipline Mathematics Date Approved March 31, 2011 General Course Description A first course in differential and integral calculus of a single variable: functions; limits and continuity; techniques and applications of differentiation and integration; Fundamental Theorem of Calculus. Primarily for Science, Technology, Engineering and Math Majors. Minimum Units 4.0 Any rationale or comments Advisories/Recommendations Course Content Definition and computation of limits using numerical, graphical, and algebraic approaches Continuity and differentiability of functions Derivative as a limit Interpretation of the derivative as: slope of tangent line, a rate of change Differentiation formulas: constants, power rule, product rule, quotient rule and chain rule Derivatives of trigonometric functions Implicit differentiation with applications, and differentiation of inverse functions Higher-order derivatives Graphing functions using first and second derivatives, concavity and asymptotes Maximum and minimum values, and optimization Mean Value Theorem Antiderivatives and indefinite integrals Applications of integration to areas and volumes Definite integral; Riemann sum Properties of the integral Fundamental Theorem of Calculus Integration by substitution Laboratory Activities Course Objectives At the conclusion of this course, the student should be able to: Compute the limit of a function at a real number; Determine if a function is continuous at a real number; Find the derivative of a function as a limit; Find the equation of a tangent line to a function; Compute derivatives using differentiation formulas; Use differentiation to solve applications such as related rate problems and optimization problems; Use implicit differentiation; Graph functions using methods of calculus; Evaluate a definite

20 integral as a limit; Evaluate integrals using the Fundamental Theorem of Calculus; and Use the definite integral to find areas and volumes Prerequisites Precalculus, or college algebra and trigonometry, or equivalent. Corequisites Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course. Notes

21 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-211 Analytic Geometry and Calculus I Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):4, 2.7 unit at CPP, 5 at CSUSM Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 4 Palomar College 5 San Bernardino Valley College 4 One community college in the San Diego area (other than Palomar) 5 at Mira Costa Local Unit Value: 5 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -The equivalent course at two of the above colleges are offered for the same amount of units, and the remaining courses differ only by one unit. -Our course includes more content than in the C-ID descriptor which many schools expect to be covered, particularly in the sciences having calculus as a prerequisite. -UC mathematics course includes a discussion section, which adds one hours of lecture per week to their course. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -Our students in many cases must take the course without access to faculty office hours. At UC, students have access to office hours with both a faculty member, and a graduate student. -Our students will be transferring to a University here they will be competing with students that took the equivalent course with 5 units, and possibly more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university. Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago. -Courses may not articulate if we remove the material necessary to reduce the number of credits. -There few community colleges that offer less units for the equivalent course.

22 -There are no universities that offer less classroom time than MSJC. Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used. -C-ID Website -Catalogs for all colleges discussed

23 Single Variable Calculus II Late Transcendentals C-ID Number MATH 221 Discipline Mathematics Date Approved March 31, 2011 General Course Description A second course in differential and integral calculus of a single variable: integration; techniques of integration; infinite sequences and series; polar and parametric equations; applications of integration. Primarily for Science, Technology, Engineering and Math Majors. Minimum Units 4.0 Any rationale or comments Advisories/Recommendations Course Content Derivatives and integrals of inverse functions and transcendental functions such as trigonometric, exponential or logarithmic; Indeterminate forms and L'Hopital's Rule; Additional techniques of integration including integration by parts and trigonometric substitution; Numerical integration; trapezoidal and Simpson's rule; Improper integrals; Additional applications such as work, volumes, arc length, area of a surface of revolution, moments and centers of mass, separable differential equations, growth and decay; Introduction to sequences and series; Multiple tests for convergence of sequences and series; Power series, radius of convergence, interval of convergence; Differentiation and integration of power series; Taylor series expansion of functions; Parametric equations and calculus with parametric curves; and Polar curves and calculus in polar coordinates. Laboratory Activities Course Objectives Upon successful completion of the course, students will be able to: Evaluate indeterminate forms using L'Hopital's Rule; Find derivatives of transcendental functions; Evaluate definite and indefinite integrals using a variety of integration formulas and techniques; Use integration to solve applications such as work or length of a curve; Evaluate improper integrals; Apply convergence tests to sequences and

24 series; Represent functions as power series; an Graph, differentiate and integrate functions in polar and parametric form. Prerequisites Corequisites Single Variable Calculus I Late Transcendentals (Math 211, CAN 18). Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course. Notes

25 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-212 Analytic Geometry and Calculus II Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):3, 2.7 unit at CPP, 4 at CSUSM Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 4 Palomar College 4 San Bernardino Valley College 4 One community college in the San Diego area (other than Palomar) 4 at Mira Costa Local Unit Value: 5 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -The equivalent courses at the above colleges differ only by one unit. -UC mathematics course includes a discussion section, which adds one hour of lecture per week to their course. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -Our students in many cases must take the course without access to faculty office hours. At UC, students have access to office hours with both a faculty member, and a graduate student. -Our students will be transferring to a University where they will be competing with UC students that were provided with more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university. Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago. -Courses may not articulate if we remove the material necessary to reduce the number of credits. -There are no universities that offer less classroom time than MSJC. Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used. -C-ID Website

26 -Catalogs for all colleges discussed

27 Multivariable Calculus C-ID Number MATH 230 Discipline Mathematics Date Approved March 31, 2011 General Course Description Vector valued functions, calculus of functions of more than one variable, partial derivatives, multiple integration, Green s Theorem, Stokes Theorem, divergence theorem. Minimum Units 4.0 Any rationale or comments Advisories/Recommendations None Course Content Vectors and vector operations in two and three dimensions; Vector and parametric equations of lines and planes; rectangular equation of a plane; Dot, cross, and triple products and projections; Differentiability and differentiation including partial derivatives, chain rule, higher-order derivatives, directional derivatives, and the gradient; Arc length and curvature; tangent, normal, binormal vectors; Vector-valued functions and their derivatives and integrals; finding velocity and acceleration; Realvalued functions of several variables, level curves and surfaces; Limits, continuity, and properties of limits and continuity; Local and global maxima and minima extrema, saddle points, and Lagrange multipliers; Vector fields including the gradient vector field and conservative fields; Double and triple integrals; Applications of multiple integration such as area, volume, center of mass, or moments of inertia; Change of variables theorem; Integrals in polar, cylindrical, and spherical coordinates; Line and surface integrals including parametrically defined surfaces; Integrals of real-valued functions over surfaces; Divergence and curl; and Green s, Stokes, and divergence theorems. Laboratory Activities Course Objectives Upon successful completion of the course, students will be able to: Perform vector operations; Determine equations of lines and planes; Find the limit of a function at a point; Evaluate derivatives; Write the equation of a tangent plane at a point; Determine differentiability; Find local extrema and

28 test for saddle points; Solve constraint problems using Lagrange multipliers; Compute arc length; Find the divergence and curl of a vector field; Evaluate two and three dimensional integrals; and Apply Green s, Stokes, and divergence theorems. Prerequisites One year of Single Variable Calculus (C-ID MATH 210 and MATH 220 OR C-ID MATH 211 and MATH 221 OR C-ID MATH 900S) Corequisites None Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course. Notes

29 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-213 Analytic Geometry and Calculus III Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):4, 2.7 unit at CPP, 5.3 at UCR Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 4 Palomar College 4 San Bernardino Valley College 4 One community college in the San Diego area (other than Palomar) 4 at Mira Costa Local Unit Value: 5 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -The equivalent courses at the above colleges differ only by one unit. -The equivalent course at many UC schools, such as UCR, UCI, UCLA offer the equivalent coursework in 5.33 credits. -UC mathematics course includes a discussion section, which adds one hour of lecture per week to their course. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -Our students in many cases must take the course without access to faculty office hours. At UC, students have access to office hours with both a faculty member, and a graduate student. -Our students will be transferring to a University where they will be competing with UC students that were provided with more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university. Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago. -There are no universities that offer less classroom time than MSJC. Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used.

30 -C-ID Website -Catalogs for all colleges discussed

31 Ordinary Differential Equations C-ID Number MATH 240 Discipline Mathematics Date Approved March 31, 2011 General Course Description The course is an introduction to ordinary differential equations including both quantitative and qualitative methods as well as applications from a variety of disciplines. Introduces the theoretical aspects of differential equations, including establishing when solution(s) exist, and techniques for obtaining solutions, including, series solutions, and singular points, Laplace transforms and linear systems. Minimum Units 3.0 Any rationale or comments Advisories/Recommendations Three semesters of calculus for science, mathematics, and engineering. Course Content Solutions of ordinary differential equations; First order DE including separable, homogeneous, exact, and linear; Existence and uniqueness of solutions; Applications of first order differential equations such as circuits, mixture problems, population modeling, orthogonal trajectories, and slope fields; Second order and higher order linear differential equations; Fundamental solutions, independence, Wronskian; Nonhomogeneous equations; Applications of higher order differential equations such as the harmonic oscillator and circuits; Variation of parameters; Laplace Transforms; Series Solutions; and Systems of Ordinary differential equations Laboratory Activities Course Objectives Upon successful completion of the course, students will be able to: Create and analyze mathematical models using ordinary differential equations; Identify the type of a given differential equation and select and apply the appropriate analytical technique for finding the solution of first order and selected higher order ordinary differential equations; Apply the existence and uniqueness theorems for ordinary differential equations; Find power series solutions to ordinary differential equations; Determine the

32 Laplace Transform and inverse Laplace Transform of functions; and Solve Linear Systems of ordinary differential equations. Prerequisites Single Variable Calculus II ()or one year of Single Variable Calculus Corequisites Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems. Sample Textbooks A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course. Notes

33 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-215 Differential Equations Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):3, 2.7 unit at CPP, 5.3 at CSUSB Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 4 Palomar College 4 San Bernardino Valley College 4 One community college in the San Diego area (other than Palomar) 4 at Mira Costa Local Unit Value: 4 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -The equivalent course at the above colleges is offered at the same number of units. -UC mathematics course includes a discussion section, which adds one hour of lecture per week to their course. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -Our students in many cases must take the course without access to faculty office hours. At UC, students have access to office hours with both a faculty member, and a graduate student. -Our students will be transferring to a University where they will be competing with students that took the course for 4 units and were provided with more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university. Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago. -There are no universities that offer less classroom time than MSJC. Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used. -C-ID Website -Catalogs for all colleges discussed

34

35 Introduction to Linear Algebra C-ID Number MATH 250 Discipline Mathematics Date Approved March 31, 2011 General Course Description This course develops the techniques and theory needed to solve and classify systems of linear equations. Solution techniques include row operations, Gaussian elimination, and matrix algebra. Investigates the properties of vectors in two and three dimensions, leading to the notion of an abstract vector space. Vector space and matrix theory are presented including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Selected applications of linear algebra are included. Minimum Units 3.0 Any rationale or comments Advisories/Recommendations A year of college calculus. Prior or concurrent course work with vector calculus or vector-intensive physics would be helpful. Course Content Techniques for solving systems of linear equations including Gaussian and Gauss-Jordan elimination and inverse matrices; Matrix algebra, invertibility, and the transpose; Relationship between coefficient matrix invertibility and solutions to a system of linear equations and the inverse matrices; Special matrices: diagonal, triangular, and symmetric; Determinants and their properties; Vector algebra for Rn; Real vector space and subspaces; Linear independence and dependence; Basis and dimension of a vector space; Matrix-generated spaces: row space, column space, null space, rank, nullity; Change of basis; Linear transformations, kernel and range, and inverse linear transformations; Matrices of general linear transformations; Eigenvalues, eigenvectors, eigenspace; Diagonalization including orthogonal diagonalization of symmetric matrices; Inner products on a real vector space; Dot product, norm of a vector, angle between vectors, orthogonality of two vectors in Rn; Angle and orthogonality in inner product spaces; and Orthogonal and orthonormal bases: Gram-Schmidt process. Laboratory Activities

36 Course Objectives Upon successful completion of the course, students will be able to: Find solutions of systems of equations using various methods appropriate to lower division linear algebra; Use bases and orthonormal bases to solve problems in linear algebra; Find the dimension of spaces such as those associated with matrices and linear transformations; Find eigenvalues and eigenvectors and use them in applications; and Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues. Prerequisites Calculus I (C-ID MATH 210, MATH 211 OR MATH 900S) Corequisites None Methods of Evaluation Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems and proofs. Sample Textbooks A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course. Notes

37 High Unit Course Justification Please complete the form and attach it to the COR in CurricUNET using the Attached Files tab. Course (Number & Title): MATH-218 Linear Algebra Transfer-Level Course (yes / no): Yes Norm Unit Value (C-ID minimum, Assist agreement with CSU or UC, other):3, 2.7 unit at CPP, 4 at CSUF Unit Value at the following local community colleges: RCCD (Riverside College, Norco College, or Moreno Valley College) 3 Palomar College 3 San Bernardino Valley College 4 One community college in the San Diego area (other than Palomar) 4 at Mira Costa Local Unit Value: 4 Justification: What is the need for and/or benefit of allocating additional units? (If more than one, please list/number separately throughout this document.) -Our course includes more content than in the C-ID descriptor. -The equivalent course at two of the above colleges is offered at the same number of units. -The colleges that offer the course at less units cover less content than our course. -UC mathematics course includes a discussion section, which adds one hour of lecture per week to their course. -CSUs offer workshops and problem solving sessions with graduate students, in many cases adding two hours of lecture to the course per week. -Our students in many cases must take the course without access to faculty office hours. At UC, students have access to office hours with both a faculty member, and a graduate student. -Our students will be transferring to a University where they will be competing with students that took the course for 4 units and were provided with more faculty contact hours. It is our responsibility to make sure that our students are prepared to compete and succeed upon transferring to university. Support Data: Success rates, state and/or other mandates/requirements. (For example, success rates for the equivalent course at other colleges with the C-ID minimum units vs. the success rates before the number of units was increased if the change in units was made fewer than 10 years ago. -Course may not articulate if we remove content in order to reduce the number of units. -There are no universities that offer less classroom time than MSJC.

38 Sources: For example, if it is required by Title 5, or other regulatory mandates, then include the section numbers and text used. -C-ID Website -Catalogs for all colleges discussed

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