Classes in math

MATH 1A Single-Variable Calculus and Analytic Geometry 4.0 units
Description: A first course in differential and integral calculus of a single variable covering limits and continuity, analyzing the behavior and graphs of functions, derivatives, implicit differentiation, higher order derivatives, related rates and optimization problems, Newton's Method, Fundamental Theorem of Calculus, and definite and indefinite integrals. PREREQUISITE: Mathematics 8B or Mathematics 11 with a grade of 'C' or better.

Student Learning Outcomes:

1. Explain and evaluate limits in general, at infinity, and at particular points. Do it algebraically, graphically and numerically, utilizing technology.
2. Use continuity to describe the behavior of a function and its differentiability.
3. Explain the concept of a derivative graphically, numerically, algebraically, and verbally.
4. Demonstrate the ability to differentiate polynomials, exponential, logarithmic, rational, implicit, and trigonometric functions. Be able to compute higher order derivatives of these functions.
5. Model and solve related rates and optimization problems.
6. Analyze and graph functions w/o a calculator. Use derivatives to identify max and min, pts. of inflection, and concavity.
7. Calculate limits using L'Hopital's Rule. Be able to determine whether it's applicable or not.
8. Use technology to estimate roots using Newton's Method.
9. Explain and apply the Fundamental Theorem of Calculus. Use it to evaluate definite and indefinite integrals. Compute basic antiderivatives.
10. Use technology to evaluate the definite integral using the Right Hand, Left Hand, and Midpoint Rules. Do Riemann sums.


MATH 1B Single-Variable Calculus and Analytic Geometry 4.0 units
Description: A second course in differential and integral calculus of a single variable covering methods of integration, applications of the integral, differential equations, parametric and polar equations, and sequences and series. (C-ID: MATH 220, MATH 900S: Math 1A + Math 1B) PREREQUISITE: Mathematics 1A with a grade of 'C' or better.

Student Learning Outcomes:

1. Identify and use the techniques and applications of differentiation and integration learned in Math 1A.
2. Evaluate definite and indefinite integrals using the substitution method, integration by parts, trigonometric substitution, and partial fraction expansion.
3. Choose an appropriate strategy for integrating a function and perform the integration.
4. Formulate and evaluate an integral to find area, volume, work, arc length, and surface area, and to solve problems found in business, economics, physics, science, statistics, and other disciplines.
5. Use technology to approximate definite integrals of functions that cannot be integrated using the above mentioned techniques.
6. Evaluate improper integrals and use them to solve applied problems.
7. Set up and solve differential equations to model applications in business, science, physics, engineeringand other disciplines.
8. Set up, compute and analyze derivatives and integrals of parametric and polar equations to find local extrema, points of inflection, intervals of increasing/decreasing, concavity, equations of tangent lines, area and arc length, both with and without the use of technology.
9. Explain the concepts of convergence, absolute convergence, conditional convergence and divergence of a series and convergence and divergence of a sequence. Use the Integral Test, Comparison Test, Limit Comparison Test, Alternating Series Test, Ratio Test and Root Test to determine convergence or divergence of a series.
10. Find the Taylor and MacLaurin Series expansion of a function centered about a given point.


MATH 1C Multivariable Calculus 4.0 units
Description: A standard third semester Calculus course covering functions of several variables, vectors, surfaces, vector-valued functions, partial derivatives, multiple and line integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem.

Student Learning Outcomes:

1. Identify, describe, and illustrate level curves, lines, planes, solids, cylinders, and quadric surfaces using three-dimensional coordinate systems.
2. Formulate, analyze, and solve problems containing vectors and use parametric equations and vector functions to describe space curves.
3. Apply differentiation and integration of vector functions to real world problems including arc length, curvature, velocity, and acceleration.
4. Apply the concepts of domain, range, evaluation, limits, and continuity to functions of more than one variable.
5. Formulate, analyze, and solve problems using partial derivatives including directional derivatives, gradient, and optimizations.
6. Calculate double and triple integrals utilizing various three-dimensional coordinate systems and Jacobian transformations.
7. Apply integration of mutilvariable functionsto real-world problems including mass, moments, center of mass, surface area, and volume.
8. Identify and sketch vector fields; find and sketch gradient fields.
9. Calculate line integrals and apply the Fundamental Theorem of Line Integrals and Green's Theorem.
10. Identify parametric surfaces; calculate surface integrals, and apply Stokes' Theorem and the Divergence Theorem.
11. Classify critical points as local extrema or saddle points. Solve extreme value problems with constraints using Lagrange multipliers.


MATH 2 Linear Algebra 3.0 units
Description: A standard one semester Linear Algebra course covering systems of linear equations, vectors and matrices, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors. (C-ID: MATH 250) PREREQUISITE: Mathematics 1C with a grade of 'C' or better.

Student Learning Outcomes:

1. Define a homogenous linear system of m equations with n unknowns and identify a sufficient condition for its nontrivial solution. Define and apply Gaussian elimination method for solving systems of linear equations.
2. Add and multiply matrices and analyze the properties of Matrix multiplication.
3. Compute the transpose, determinant, and inverse for a given matrix and prove basic theorems relating to deteminants and matrices. Evaluate the determinants of matrices and apply Cramer's rule to solve linear systems.
4. Define subspaces in R-2 and R-3 and inner products; determine the dimension of a subspace and analyze the function that maps two vectors from a vector space to a scalar and prove basic theorems about properties of subspaces.
5. Differentiate between linearly dependent and linearly independent sets of vectors and find a basis of the subspace; construct orthogonal and orthonormal bases using the Gram-Schmidt Process for a given basis.
6. Define eigenvalues and eigenvectors and perform at least one method to calculate eigenvalues, eigenvectors, and eigenspaces for both matrices and linear transformations. Construct the orthogonal diagonalization of a symmetric matrix.
7. Define linear transformation, transformations from R to R, matrix transformations, one-to-one, kernel, range, rank, nulity and isomotphism, and solve application problems using the properties of linear mappings: image and kernel.


MATH 2C Differential Equations 3.0 units
Description: An introductory course in differential equations that covers: first order differential equations including separable, linear, exact, homogeneous, bernoulli and Euler's Method; second order differential equations including homogeneous, nonhomogeneous, variation of parameters, method of undetermined coefficients and reduction of order; series solutions to differential equations; Laplace Transforms; linear systems; and if time, Fournier Analysis; and applications thereof. (C-ID: MATH 240) PREREQUISITE: Mathematics 1C with a grade of 'C' or better.

Student Learning Outcomes:

1. Formulate, analyze and solve first, second, and higher order differential equations.
2. Solve applied problems involving differential equations.
3. Use technology to find numerical approximations to solutions of differential equations and to analyze graphs of solutions of differential equations.


MATH 5 Introduction to Statistics 3.0 units
Description: Descriptive analysis and presentation of either single-variable data or bivariate data, probability, probability distributions, normal probability distributions, sample variability, statistical inferences involving one and two populations, analysis of variance, linear correlation and regression analysis. Statistical computer software will be extensively integrated as a tool in the description and analysis of data. The instructor will be using and supporting a TI-83 Plus graphing calculator in all classroom demonstrations. PREREQUISITE: MATH 233, or MATH 240, or MATH 233A and MATH 233B, or MATH 242 with a grade of 'C' or better.

Student Learning Outcomes:

1. Describe and analyze data using descriptive statistics including histograms, frequency tables, stem-and-leaf diagrams, boxplots, mean, median, mode, and standard deviation. Be able to distinguish among different scales of measurement and their implications.
2. Demonstrate proficiency with calculations of basic probabilities for simple events.
3. Identify the difference between discrete and continuous random variables. Be able to calculate the mean and variance of a discrete distribution.
4. Calculate probabilities using a normal distribution or graphing calculator.
5. Interpret the Central Limit Theorem and apply the concept to examples.
6. Create and interpret confidence intervals estimates of population means and proportions.
7. Identify the basic concepts of hypothesis testing including Type I and Type II errors. Employ hypothesis test procedures to test claims about single population means and proportions, and two population means and proportions. Select the appropriate technique (p-value, t-test, z-test) for analyzing the hypothesis test. Be able to interpret the result of the hypothesis test in words.
8. Employ linear correlation and regression to model simple linear relationships.
9. Utilize statistical software to analyze and interpret data.
10. Demonstrate a synthesis of concepts learned throughout the semester by a group project, which will require students to formulate a survey, collect data, analyze data, and derive inferences from the data.
11. Discuss sampling methods and identify the standard methods of obtaining data and identify advantages and disadvantages of each.
12. Do application problems using data from disciplines including business, social sciences, psychology, life science, health science, and education.


MATH 6 Calculus for Business/Social Science 3.0 units
Description: This course applies the fundamental principles and techniques of calculus to problems in business, economics, the life sciences and the social sciences. Topics will include limits, and differentiation and integration of linear, quadratic, polynomial, exponential and logarithmic functions. This course is not intended for students majoring in engineering, the physical sciences or math. Using a calculator is required. Graphing calculator is recommended. (C-ID: MATH 140) PREREQUISITE: Skills equivalent to intermediate algebra or appropriate placement.

Student Learning Outcomes:

1. Analyze properties of quadratic functions and their graphs. Applications in business, social sciences and life sciences will be chosen to demonstrate knowledge in polynomial and rational functions.
2. Find derivatives of polynomials, rational, exponential, and logarithmic functions. Use the rules for sums as well as use product and quotient and chain rules to solve problems involving complex equations.
3. Use calculus to 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.
4. Analyze the marginal cost, profit and revenue when given the appropriate function; determine maxima and minima in optimization problems using the derivative; use derivatives to find rates of change and tangent lines; and use calculus to analyze revenue, cost, and profit. Apply this to applications in business, economics, and the life sciences.
5. Work with the definite integral as a limit of a sum and relate it to the fundamental theorem of calculus.
6. Find definite and indefinite integrals by using general formulas, substitution, integration by parts, integral tables, and other integration techniques. Use integration techniques and apply them to business and economic applications and to the life sciences.


MATH 7 Finite Mathematics 3.0 units
Description: Systems of linear equations and matrices, introduction to linear programming, finance, counting techniques and probability, properties of probability and applications of probability. PREREQUISITE: Mathematics 233 OR Mathematics 235 OR Mathematics 240 OR equivalent with a grade of "C" or better.

Student Learning Outcomes:

1. Demonstrate proficiency in using rectangular coordinates, graphing linear equations in two variables, applying linear equations to determine break-even point, and market price for supply/demand equations and other applications found in business and social science.
2. Solve systems of equations using substitution, elimination, and matrix methods. Solve application problems.
3. Demonstrate skills in basic matrix algebra to include addition, subtraction, multiplication and inverses, both by hand and with a calculator.
4. Apply a geometric approach (graphing) to solve linear programming problems limited to two variables. Solve application problems.
5. Apply the Simplex Method (matrix method) to solve linear programming (maximization and minimization) problems in standard form. Solve application problems.
6. Demonstrate skill in solving finance problems to include simple interest, compound interest, ordinary annuities, future value, sinking funds, and amortization. Solve application problems related to topics mentioned above.
7. Use properties of sets, the Multiplication Principle, combinations, permutations, and other counting techniques to determine probability. Use/ apply DeMorgan's laws. Determine the conditional probability of an event. Solve application problems.


MATH 8A First Half of Precalculus 4.0 units
Description: Math 8A prepares the student for the study of calculus by providing important skills in algebraic manipulation, interpretation, and problem solving at the college level. Topics will include basic algebraic concepts, complex numbers, equations and inequalities of the first and second degree, functions, and graphs, linear and quadratic equations, polynomial functions, exponential and logarithmic functions, systems of equations, and matrices. PREREQUISITE: Mathematics 240 with a grade of 'C' or better or skills equivalent to those in an Intermediate Algebra course or appropriate placement.

Student Learning Outcomes:

1. Solve a wide variety of equations and inequalities including absolute value, radical, rational, exponential, logarithmic and polynomial.
2. Identify and perform transformations on the graphs of elementary (radical, absolute value, etc.), polynomial (linear, quadratic, cubic), rational, exponential, and logarithmic functions.
3. Solve systems of equations and inequalities using graphing, elimination, substitution techniques, matrix algebra, and determinants.
4. Explain the concept of a function, perform the arithmetic operations of functions, identify the domain of a function, and analyze graphs of functions.
5. Recognize the relationship between inverse functions graphically and through composition.
6. Recognize functional patterns in data and apply functions to model real-world applications.
7. Graph polynomial functions and characterize the real and complex zeros of polynomials.
8. Locate the asymptotes and zeros of rational functions analytically and graph a rational function.


MATH 8B Second Half of Precalculus 4.0 units
Description: Math 8B prepares students for the study of calculus by providing important skills in algebraic manipulation, interpretation, and problem solving at the college level. Topics will include trigonometric functions, identities, inverse trigonometric functions, and equations; applications of trigonometry, vectors, complex numbers, polar and parametric equations; sequences, series, and mathematical induction; conic sections. PREREQUISITE: Mathematics 8A with a grade of 'C' or better.

Student Learning Outcomes:

1. Find the trigonometric values of any angle or real number and the inverse trigonometric values of real numbers.
2. Graph the basic trigonometric functions and apply changes in period, phase, and amplitude to generate new graphs. Graph inverse trigonometric functions.
3. Solve trigonometric equations, triangles, and applications, including applying the Law of Sines and the Law of Cosines.
4. Manipulate trigonometric expressions and verify trigonometric identities.
5. Calculate powers and roots of complex numbers using DeMoivre's Theorem.
6. Model physical problems using vectors. Decompose vectors into components, add and subtract vectors, multiply vectors using the dot and cross products.
7. Convert between polar and rectangular coordinates. Graph polar and parametric equations.
8. Identify, manipulate, graph, and apply conic sections.


MATH 11 Integrated Precalculus 8.0 units
Description: Math 11 is a blend of Math 8A and 8B Precalculus classes. Math 11 prepares students for the study of calculus by providing important skills in algebraic manipulation, interpretation, and problem solving at the college level. Topics will include basic algebraic concepts, complex numbers, equations and inequalities of the first and second degree, functions and graphs, linear and quadratic equations, polynomial functions, exponential and logarithmic functions, systems of equations, matrices and determinants, trigonometric functions, identities, inverse trigonometric functions, applications of trigonometry, vectors, polar and parametric equations, sequences, series, conic sections, and mathematical induction. PREREQUISITE. Mathematics 240 with a grade of 'C' or better, or appropriate placement.

Student Learning Outcomes:

1. Solve a wide variety of equations and inequalities including absolute value, radical, rational, exponential, logarithmic and polynomial.
2. Identify and perform transformations on the graphs of elementary (radical, absolute value, etc.), polynomial (linear, quadratic, cubic), rational, exponential, and logarithmic functions.
3. Solve systems of equations and inequalities using graphing, elimination, substitution techniques, matrix algebra, and determinants.
4. Explain the concept of a function, perform the arithmetic operations of functions, identify the domain of a function, and analyze graphs of functions.
5. Recognize the relationship between inverse functions graphically and through composition.
6. Recognize functional patterns in data and apply functions to model real world applications.
7. Graph polynomial functions and characterize the real and complex zeroes of polynomials.
8. Locate the asymptotes and zeroes of rational functions analytically and graph a rational function.
9. Find the trigonometric values of any angle or real number and the inverse trigonometric values of real numbers.
10. Graph the basic trigonometric functions and apply changes in period, phase, and amplitude to generate new graphs. Graph inverse trigonometric functions.
11. Solve trigonometric equations, triangles, and applications, including application of the Law of Sines and the Law of Cosines.
12. Manipulate trigonometric expressions and verify trigonometric identities.
13. Calculate powers and roots of complex numbers using DeMoivre's Theorem.
14. Model physical problems using vectors. Decompose vectors into components, add and subtract vectors, multiply vectors using the dot and cross products.
15. Convert between polar and rectangular coordinates. Graph polar and parametric equations.
16. Identify, manipulate, graph, and apply conic sections.


MATH 12 Mathematics for Elementary Teachers 3.0 units
Description: This course is intended for students preparing for a career in elementary school teaching. Emphasis will be on the structure of the real number system, numeration systems, elementary number theory, and problem solving techniques. Technology will be integrated throughout the course. PREREQUISITE: High School Geometry and Math 240 (Algebra 2) or Math 242 (Algebra for Statistics) or skills equivalent to Intermediate Algebra. All courses must be completed with a grade of 'C' or better.

Student Learning Outcomes:

1. Identify, describe, compare and contrast patterns, number relationships, prime numbers, composite numbers, and operation relationships of real numbers.
2. Identify, describe, compare and contrast algorithms to find estimates and exact answers to problems involving whole numbers, integers, and rational numbers.
3. Identify, describe, compare and contrast patterns and models of integer and arithmetic operations.
4. Identify, describe, compare and contrast problem-solving methodologies involving whole numbers, integers, and rational numbers.


MATH 14 Math for the Liberal Arts 3.0 units
Description: Survey of selected topics from contemporary mathematics to introduce the liberal arts student to a variety of mathematical ideas, methods and historical trends. Topics include systems of numeration, logic, set theory, mathematical modeling, geometry, trigonometry, mathematics of finance, probability and statistics. PREREQUISITE: Math 240 or Math 242 with a grade of 'C' or better.

Student Learning Outcomes:

1. Demonstrate literacy in a variety of mathematical topics including set theory, logic, mathematical modeling, geometry, trigonometry, systems of numeration, probability and statistics.


MATH 16 Discrete Mathematics 4.0 units
Description: Presents discrete mathematical systems including methods of proof that shape the foundations of computer science. Includes propositional logic, set and number theory, Boolean Algebra, deductive and inductive proof, functions and relations, combinatorics, discrete probability, graph theory and network models, and efficiency of algorithms. PREREQUISITE: Mathematics 8B with a grade of 'C' or better or equivalent skills. ADVISORY: CSIS 5 or CSIS 45 with a grade of 'C' or better or equivalent skills.

Student Learning Outcomes:

1. Evaluate the truth and falsity of mathematical statements employing deductive and inductive proof techniques.
2. Analyze the relationships among counting techniques (combinatorics), discrete probability, sets, Boolean algebra, and propositional logic.
3. Evaluate graphs, trees, and networks in terms of efficiency, redundancy, and similiarity.


MATH 22 Field Work and Service 0.5 units
Description: Supervised field work within the college and with local agencies. Students serve in useful group activities in leadership roles prescribed for them by faculty or community agencies. A maximum of six units may be completed. This is a pass/no pass course. REQUIRED: Learning contracts must be filled out and signed by the student and the supervising instructor.



MATH 23 Independent Study 1.0 units
Description: Designed to afford selected students specialized opportunities for exploring areas at the independent study level. The courses may involve extensive library work, research in the community, or special projects. May be repeated until six units of credit are accrued. This course has the option of a letter grade or pass/no pass. REQUIRED: The study outline prepared by the student and the instructor must be filed with the department and the dean.



MATH 205 Elementary Algebra 5.0 units
Description: This course is a standard beginning algebra course, including algebraic expressions, linear equations and inequalities in one variable, graphing, equations and inequalities in two variables, integer exponents, use of a scientific calculator, polynomials, rational expressions and equations, radicals and rational exponents, and quadratic equations. Mathematics 205, 205A and 205B, and 206 have similar course content. This course may not be taken by students who have completed Mathematics 205B or 206 with a grade of "C" or better. This course may be taken for Mathematics 205B credit (2.5 units) by those students who have successfully completed Mathematics 205A with a grade of "C" or better. PREREQUISITE: MATH 402 with a grade of 'Pass' or with a 'C' or better, or assessment test recommendation.

Student Learning Outcomes:

1. Simplify and evaluate expressions. Solve linear equations and inequalities in one variable and their applications.
2. Evaluate and solve formulas.
3. Graph linear equations and inequalities in two variables.
4. Solve systems of equations and inequalities in two variables and their applications.
5. Apply the laws of exponents to algebraic expressions. Use scientific notation and a scientific calculator.
6. Define a polynomial and perform the operations of addition, subtraction, multiplication, and division of polynomials.
7. Factor polynomials and solve polynomial equations in one variable.
8. Simplify and add, subtract, multiply, and divide with rational expressions.
9. Determine square roots, simplify radicals, and perform basic operations with radicals
10. Solve quadratic equations by using the quadratic formula.


MATH 205A First Half of Elementary Algebra 2.5 units
Description: This course is the first half of the Elementary Algebra course. It will cover signed numbers, evaluation of expressions, ratios and proportions, solving linear equations, and applications. Graphing of lines, the slope of a line, graphing linear equations, solving systems of equations, basic rules of exponents, and operations on polynomials will be covered. PREREQUISITE: Math 402 with a grade of 'Pass' or with a 'C' or better, or assessment test recommendation. ADVISORY: Concurrent enrollment in Guidance 563A is advised.

Student Learning Outcomes:

1. Identify, describe, and demonstrate ability to work with fractions and signed numbers.
2. Apply addition and multiplication properties in solving linear equations
3. Formulate and solve word problems including use of formulas, ratios, and proportions.
4. Identify and solve linear inequalities, Demonstrate the ability to graph the interval on the number line.
5. Analyze and interpret graphs, plot ordered pairs of numbers,
6. Identify and sketch the graph of the linear equation.
7. Calculate the slope of the line and apply three forms of the linear equation to establishing the equation that fits a data.
8. Demonstrate the ability to graph linear inequalities in two variables
9. Apply the graphing, substitution, and elimination methods in solving systems of linear equations
10. Apply acquired skills in solving systems of linear inequalities
11. Identify bases and exponents, demonstrate ability to use product rule for exponents.


MATH 205B Second Half of Elementary Algebra 2.5 units
Description: This course contains the material covered in the second half of the Elementary Algebra Course. It will cover factoring polynomials, solving quadratic equations by factoring, rational expressions, radicals, and solving quadratic equations. In addition, the course will review applications involving linear equations of one and two variables, finding slopes and graphing linear equations, solving systems of equations with two variables, and solving linear inequalities. Math 205, 205A and 205B, and 206 have similar course content. This course may not be taken by students who have completed Math 205 or 206 with a grade of 'C' or better. PREREQUISITE: Math 205A with a grade of 'C' or better. ADVISORY: Concurrent enrollment in Guidance 563B is advised.

Student Learning Outcomes:

1. Apply the laws of exponents to algebraic expressions.
2. Find the slope and equation of a line.
3. Graph linear equations.
4. Solve systems of equations in two variables and their applications.
5. Define a polynomial andperform the operations of addition, subtraction, multiplication, and division of polynomials.
6. Factor polynomials and solve polynomial equations in one variable.
7. Simplify and perform operations with rational expressions.
8. Determine square roots, simplify radicals, and perform basic operations with radicals.
9. Solve quadratic equations by using the quadratic formula
10. Solve applications of linear equations including geometric applications.


MATH 208 Plane Geometry 3.0 units
Description: This course introduces the vocabulary and principles of Euclidean Geometry. Methods of proof including inductive and deductive reasoning will be developed. Concepts of congruence and similarity, angles, lines, polygons, and circles will be covered. Additional topics such as solid geometry, analytical geometry, transformations, and basic trigonometry may be included as time allows. PREREQUISITE: Math 430 or equivalent with a grade of "C" or better.

Student Learning Outcomes:

1. Students will write geometric proofs, including inductive and deductive proofs, and proof by contradiction.
2. Students will prove basic theorems involving congruence and similarity for triangles.
3. Students will prove and use theorems involving the properties of parallel lines, quadrilaterals, and circles.
4. Students will derive and solve problems involving perimeters, circumferences, areas, surface areas , and volumes of common geometric figures.
5. Students will prove the Pythagorean Theorem and apply it to right triangle problems.


MATH 215 Statistics Support 2.0 units
Description: A review of the core prerequisite skills needed for Math 5: Introduction to Statistics. Intended for students who are concurrently enrolled in Math 5: Introduction to Statistics at Gavilan College. The course will focus on core concepts from Algebra and Statistics that are needed to support success in transfer-level Statistics. Topics include operations on real numbers including order of operations, fractions, decimals, percentages, exponents and logarithms, correct selection and implementation of statistical formulas, review of the Cartesian coordinate system and written interpretation of slope and intercept of linear equations, exploratory analysis of categorical, quantitative, single variable and bivariate data, discrete and normal probability, support for graphing calculator usage and for statistical software. This course is appropriate for students confident in beginning algebra who need support for intermediate algebra skills essential for statistics. This course is Pass/No Pass only. Non-degree applicable. Prerequisite: Appropriate placement. Corequisite: Math 5: Introduction to Statistics.

Student Learning Outcomes:

1. Demonstrate proficiency in formulating questions which can be addressed with data. Organize, display, and analyze relevant data to address these questions and communicate results.
2. Demonstrate proficiency with calculations using statistical formulas and notation commonly encountered in a Math 5 course.
3. Demonstrate proficiency in transfer-level mathematics study skills, including reading and notetaking using a statistics textbook, writing clear statistical interpretations, utilizing time management for completion of labs and assignments, and preparing for written examinations.


MATH 216 Business Calculus Support 2.0 units
Description: A review of the core prerequisite skills needed in business calculus. Intended for students who are concurrently enrolled in Math 6: Calculus for Business, Economics, and Social Sciences at Gavilan College. Topics include the following: polynomial, rational and radical expressions and equations, linear and quadratic equations and inequalities, exponential and logarithmic expressions and equations, functions, and graphs of linear, quadratic, exponential, and logarithmic functions. This course is appropriate for students who are confident in their graphing and beginning algebra skills. This course is Pass/No Pass only. Non-degree applicable. Prerequisite: Appropriate placement. Corequisite: Math 6: Calculus for Business, Economics, and Social Sciences.

Student Learning Outcomes:

1. Simplify expressions.
2. Solve equations and inequalities.
3. Graph equations and functions.


MATH 218 Precalculus Support 1.0 units
Description: A review of the core prerequisite skills, competencies, and concepts needed in Math 8A: First Half of Precalculus. Intended for STEM majors who are concurrently enrolled in MATH 8A: First Half of Precalculus, at Gavilan College. Topics include: a review of computational skills developed in intermediate algebra, factoring, operations on rational and radical expressions, absolute value equations and inequalities, exponential and logarithmic expressions and equations, and an in-depth focus on functions including composition, inverses and graphs. This course is appropriate for students who are confident in their graphing and beginning algebra skills. This course is Pass/No Pass only. Non-degree applicable. Prerequisite: Appropriate placement. Corequisite: Math 8A: First Half of Precalculus.

Student Learning Outcomes:

1. Simplify expressions.
2. Solve equations and inequalities.
3. Solve systems of two equations.
4. Graph a function and identify its defining elements (including domain and range).


MATH 219 Preparation for Calculus Bootcamp 1.0 units
Description: This is a course for students who wish to refresh or re-learn fundamental algebraic or pre-calculus concepts. The focus is on polynomial, trigonometric, exponential and logarithmic functions and equations and the graphs of these functions. This class is preparation for Math 8B, Math 1A, or Math 1B. This is a Pass/No Pass course.

Student Learning Outcomes:

1. Students will be able to solve polynomial equations and applications of polynomial functions.
2. Students will be able to prove trigonometric identities and solve trigonometric equations.
3. Students will be able to graph and transform trigonometric functions.
4. Students will be able to solve exponential and logarithmic equations and apply exponential and logarithmic functions to real life problems.


MATH 225 Math intense review for pre-calculus 1.0 units
Description: An intense mathematics course designed for those students who need to refresh the fundamental math concepts needed for transfer level classes. The primary emphasis is on percentages, algebraic expressions, linear/quadratic equations and applications, slopes of the lines, polynomials, graphing, and functions plus working with data. This is a pass/no pass course. Units earned in this course do not count toward the associate degree and/or certain certificate requirements. This class is an intense preparation for Math 242, Math 5, Math 6, Math 7 and Math 8A.

Student Learning Outcomes:

1. Analyze and solve linear equations in one and two variables
2. Identify and analyze functions and find their domains and ranges.
3. Identifying and evaluating slope of a line in real world problem
4. Solve a variety of problems involving applications of linear and quadratic functions.
5. Identify and solve quadratic equations.
6. Graph linear and non-linear relations and utilize the graph in problem solving


MATH 233 Intermediate Algebra 5.0 units
Description: Review of basic concepts, linear equations and inequalities, graphs and functions, systems of linear equations, polynomials and polynomial functions, factoring, rational expressions and equations, roots, radicals, and complex numbers, solving quadratic equations, exponential and logarithmic functions, and problem solving strategies. Mathematics 233, 233A, and 233B have similar course content. This course may not be taken by students who have completed Mathematics 233B with a grade of 'C' or better. This course may be taken for Mathematics 233B credit (2.5) units by those students who have successfully completed Mathematics 233A with a grade of 'C' or better. PREREQUISITE: Mathematics 205 or Mathematics 205A and 205B or Mathematics 206 with a grade of 'C' or better. The instructor will be using and supporting TI-83 Plus graphing calculator in all classroom demonstrations.

Student Learning Outcomes:

1. Analyze a variety of problems involving contemporary applications of linear, quadratic, exponential, logarithmic, and rational functions. Such applications include, but are not limited to bacterial growth, radioactive decay, earthquakes, compound and simple interest, and variation.
2. Determine and implement an appropriate method of solution for these problems.
3. Graph linear, quadratic logarithmic, and exponential functions, and utilize the graph in problem solving.
4. Solve moderately complex equations and inequalities, some of which they will set up.
5. Demonstrate proficiency with a scientific calculator.


MATH 233A First Half of Intermediate Algebra 2.5 units
Description: The course will start with a review of basic concepts and then cover the following topics with an emphasis on applications and problem solving strategies: solving linear and absolute value equations; solving linear and compound inequalities; equations and graphs of lines; functions and function notation including composition of functions; solving systems of linear equations and inequalities; operations with polynomials; factoring polynomials; and solving polynomial equations. PREREQUISITE: Completion of Mathematics 205 or the equivalent with a grade of 'C' or better.

Student Learning Outcomes:

1. Analyze a variety of problems involving contemporary applications of linear and quadratic functions and determine and implement an appropriate method of solution for these problems.
2. Graph linear equations and inequalities and utilize the graphs in problem solving.
3. Set up and solve linear and compound inequalities using algebra and graphs. Determine appropriate use of the algebra and graphs to solve applied problems.
4. Analyze problems to determine the most appropriate method to use when solving a given system.
5. Demonstrate proficiency with a scientific calculator and use the calculator in solving various problems.
6. Use function operations and function notation to add, subtract, multiply, divide, and compose polynomials.


MATH 233B Second Half of Intermediate Algebra 2.5 units
Description: This course will start with a review factoring polynomials, and then cover the following topics with an emphasis on applications and problem solving strategies: solving polynomial equations by factoring; adding, subtracting, multiplying, dividing and simplifying rational expressions and solving rational equations; adding, subtracting, multiplying, dividing and simplifying roots, radicals and complex numbers and solving radical equations; working with composition of functions and inverse functions, working with exponential and logarithmic functions, equations and expressions; employing various methods of solving quadratic equations and inequalities; and graphing quadratic functions. PREREQUISITE: Completion of MATH 233A with a grade of 'C' or better.

Student Learning Outcomes:

1. Analyze a variety of problems involving contemporary applications of linear, quadratic, exponential, logarithmic, and rational functions, and determine and implement an appropriate method of solution for these problems.
2. Graph quadratic, logarithmic, and exponential functions, and identify and describe attributes of the graph such as x- and y-intercepts, domain, range, max and min.
3. Analyze the graph of a given function, identify the function as linear, quadratic, logarithmic, exponential or other, and utilize the graph in solving applied problems.
4. Differentiate between an expression or equation; identify the equation or expression aslinear, quadratic, rational, radical, exponential or logarithmic; and determine and implement an appropriate strategy to simplify if it is an expression or solve if it is an equation.
5. Set up and solve linear and non-linear inequalities both algebraically and graphically.
6. Demonstrate proficiency with a scientific calculator.


MATH 235 Integrated Algebra 7.5 units
Description: This is an intermediate algebra course with an emphasis on word problems and real life applications. The focus will be on linear equations and inequalities, graphs and functions, systems of equations, polynomials and polynomial functions/equations, factoring, rational expressions and equations, roots, radicals, complex numbers, exponential and logarithmic functions, and problem solving strategies. Prerequisite: Appropriate Placement

Student Learning Outcomes:

1. Simplify and evaluate algebraic expressions. Solve linear equations and inequalities in one variable. Evaluate and solve formulas.
2. Analyze, set up and solve quadratic, exponential, logarithmic, and rational equations.
3. Analyze and solve problems involving applications of linear, quadratic, exponential, logarithmic, and rational functions.
4. Graph linear, quadratic, logarithmic, and exponential functions and be able to utilize the graphs in problem solving.
5. Simplify radicals, perform operations with radicals. Analyze and solve radical equations.
6. Demonstrate proficiency with a scientific calculator.
7. Analyze and translate verbal expressions into algebraic expressions. Use symbolic language to name algebraic structures.
8. Formulate, analyze, and solve real life application problems.


MATH 240 Algebra II 5.0 units
Description: This is a second course of algebra and is designed for STEM and other math based majors. It will cover solving systems of equations with matrices, graphs and functions, absolute value equations and inequalities, radical, quadratic, exponential and logarithmic expressions and functions, complex numbers, conic sections, and problem solving strategies. PREREQUISITE: Math 430 with a grade of C or better, or Math 205, Math 205B, or Math 233A with a grade of C or better, or assessment test recommendation.

Student Learning Outcomes:

1. Solve absolute value equations and inequalities.
2. Analyze and solve radical, quadratic, exponential, and logarithmic equations, as well as systems of linear equations using matrices. Set up equations in all of the above to solve application problems, including investment, solution mixture, distance, population growth, and carbon dating.
3. Given a graph, equation or list, identify domain, range, points on the graph and whether a graph depicts a function.
4. Graph quadratic, logarithmic, and exponential functions and be able to utilize the graphs in problem solving
5. Simplify and perform operations with radicals expressions. Use properties of exponents and logarithms to simplify exponential and logarithmic expressions.
6. Demonstrate proficiency with a scientific calculator
7. Identify, analyze and graph conic sections.
8. Analyze and translate verbal Expressions into Algebraic. Use symbolic language to name algebraic structures.


MATH 242 Algebra for Statistics 6.0 units
Description: Math 242 is for students whose educational plan includes ONLY Math 5 (transfer-level Statistics). If your major is math, science, engineering, computer science, business, etc., and/or your educational plan includes any transfer-level math class other than Math 5, or you are unsure about your major, you should take Math 240. Math 240 and Math 242 are not equivalent. Math 242 prepares students for transfer-level Statistics (Math 5) by covering core concepts from Algebra and Statistics that are needed to understand the basics of college level statistics. Topics include operations on real numbers, solving equations, functions, inequalities, radicals, exponential and logarithmic functions, exploratory analysis of categorical, quantitative, single variable and bivariate data, and probability. PREREQUISITE: Appropriate placement.

Student Learning Outcomes:

1. Graph linear, logarithmic, and exponential functions and utilize the graphs in problem solving.
2. Given a graph, equation or list, identify domain, range, points on the graph and whether a graph depicts a function. Given a function, find it's inverse.
3. Simplify and perform operations with linear, radical, logarithmic and exponential expressions. Solve linear equations and inequalities, radical, logarithmic and exponential equations. Set up equations in all of the above to solve application problems.
4. Calculate probabilities, including obtaining normal probabilities using tables and technology.
5. Describe and analyze data using descriptive statistics including histograms, frequency tables, stem-and-leaf diagrams, box plots, mean, median, mode, and standard deviation, with and without technology.
6. Formulate questions that can be addressed with data, then organize, display and analyze the relevant data to address these questions and communicate the results.
7. Investigate relationships in bivariate quantitative data and determine an appropriate mathematical model for that data. Using technology, compute the appropriate regression model, assess the validity of that model, and communicate findings;


MATH 400 Elements of Arithmetic 3.0 units
Description: This course covers essential arithmetic operations, whole numbers, integers, fractions, decimals, ratio, proportion, percent, applications of arithmetic, and critical thinking, as well as math-specific study skills. This is a pass/no pass course, with pass being given for mastery of the content. Units earned in this course do not count toward the associate degree and/or other certain certificate requirements.

Student Learning Outcomes:

1. Perform basic operations with whole numbers, fractions, and decimals
2. Perform basic operations with integers, signed fractions and decimals+ utilize the rules for completing these operations
3. Perform the conversion from percent to decimal, from percent to fraction andbackwards
4. Solve basic percentage problems utilizing the proportional method.
5. Be able to identify and apply right strategies for solving real life percent problems.
6. Be able to solve percent problems and apply these strategies to solve real live problems
7. Utilizing proportion properties for solving application problems


MATH 402 Pre-Algebra 3.0 units
Description: This course covers operations with integers, fractions, decimals and associated applications, ratio, proportion, geometry, and measurements with the emphasis on critical thinking and applications. Elementary algebra topics such as variables, expressions, and solving equations are introduced. This is a pass/no pass course where pass is given for mastery of the above topics. The mastery level is set by the department. PREREQUISITE: Completion of Math 400 with a grade of 'C' or better OR completion of Math 400 with a grade of 'P' OR appropriate assessment test score.

Student Learning Outcomes:

1. Perform basic operations with whole numbers, integers , fractions, and decimals without the aid of a calculator.
2. Analyze a variety of problems, decide on a correct method or strategy of solution, implement the strategy to solve the problems, and evaluate solution to determine if it is reasonable using estimation skills.
3. Simplify algebraic expressions and solve equations involving integers, fractions, and decimals without the aid of a calculator.
4. Set up and solve applied problems involving proportion, ratio, unit conversion, and percents.
5. Understand basic geometric properties involving lines, angles, and other geometric figures and use these properties to solve problems. Compute perimeter, area, and volume of geometric figures.


MATH 411 Integrated Pre-Algebra 7.0 units
Description: This course is a blend of standard Elements of Arithmetic and Pre-Algebra courses with the focus on operations with whole numbers, fractions, percentages, proportions, and signed numbers. Algebraic topics such as variables, expressions, and solving basic linear equations and applications are introduced. This is a pass/no pass course where pass is given for mastery of the above topics. The mastery level is set by the department. ADVISORY: MATH 414

Student Learning Outcomes:

1. Perform basic operations with whole numbers, integers, fractions and decimals w/o aid of a calculator.
2. Implement the critical thinking strategies to solve the real life problems and analyze/evaluate the solution with respect to the context of the problem.
3. Determine and implement an appropriate method ofsolution for real life problems
4. Simplify algebraic expressions and solve linear equations involving integers, fractions, and decimals.
5. Set up and solve applied problems involving proportion, ratio, and percents.
6. Identify and analyze basic geometric shapes and be able to compute their perimeters, areas, and volumes.


MATH 412 Math Refresher 0.5 units
Description: A developmental intensive math course designed to be a refresher for students who wish to review basic math concepts before enrolling in transfer level Math courses. The primary focus is on operations with whole numbers, fractions, decimals and percentages. This is a pass/no pass course. Units earned in this class do not count toward the associate degree and/or certain certificate requirements.

Student Learning Outcomes:

1. Perform basic operations with whole numbers, fractions, decimals, and signed numbers without the use of a calculator
2. Utilize math specific study skills and test taking strategies
3. Solve basic percentage problems using proportions and equations


MATH 412A Math Refresher Part 1 0.5 units
Description: An intensive math course designed to be a refresher for students who wish to review fundamental math concepts to get the support in the current class. The primary focus is on operations with whole numbers, fractions, decimals and percentages. This is a pass/no course. Units earned in this class do not count towards an Associate's Degree or certain certificate requirements.

Student Learning Outcomes:

1. Perform basic operations with whole numbers, fractions, decimals, and signed numbers without the use of calculators.
2. Utilize math specific study skills and test taking strategies.


MATH 412B Math Refresher Part 2 0.5 units
Description: An intensive math course designed to be a refresher for students who wish to review fundamental math concepts to get the support in the current class. The primary focus is on operations with percentages, proportions, equations, and text problems. This is a pass/no course. Units earned in this class do not count towards an Associate's Degree or certain certificate requirements.

Student Learning Outcomes:

1. Solve percentage problems using proportions and equations
2. Solve problems with fractions, decimals, and signed numbers.
3. Utilize math specific study skills and test taking strategies


MATH 413 Math Immersion Review - Basic Concepts Level 1 1.0 units
Description: A remedial mathematics course designed for those students who need to learn, or re-learn, the fundamental concepts of math. The primary focus is on operations with whole numbers, fractions, decimals, percentage and real life problems. This is a pass/no pass course. Units earned in this course do not count toward the associate degree and/or certain certificate requirements. This class is an intense preparation for Math 402, Math 430 or Math 411 and Math 235.

Student Learning Outcomes:

1. Perform Basic operations with whole numbers, fractions, decimals and signed numbers w/o the use of a calculator.
2. Solve basic percentage problems using a variety of strategies.
3. Formulate and solve word problems using a variety of strategies
4. Identify and discriminate algebraic structures


MATH 414 Math Immersion Review - Basic Concepts Level 2 1.0 units
Description: A developmental immersion math course designed for those students who need to learn, re-learn, or re-fresh the fundamental concepts of Math. The primary emphasis is on fractions, signed numbers, linear equations, algebraic structures and word problems. This class is an intense preparation for Math 402, Math 411, Math 430 and Math 235. This is a pass/no pass course. Units earned in this course do not count toward the associate degree or certain certificate requirements.

Student Learning Outcomes:

1. Perform Basic operations with fractions and solve linear equations involving fractions
2. Apply addition and multiplication properties to solving linear equations.
3. Formulate and solve word problems using a variety of strategies
4. Name algebraic structures using the order of operations
5. Identify and discriminate algebraic structures


MATH 415 Math Immersion Review - Algebraic Concepts 1.0 units
Description: An intense mathematics course designed for those students who need to refresh the fundamental math concepts needed for transfer level classes. The primary emphasis is on percentages, algebraic expressions, linear/quadratic equations and applications, slopes of lines, polynomials, graphing, and functions plus working with data. This is a pass/no pass course. Units earned in this course do not count toward the associate degree and/or certain certificate requirements. This class is an intense preparation for Math 5, Math 6, Math 7, and Math 8A.

Student Learning Outcomes:

1. Identify and analyze functions and find their domains and ranges.
2. Analyze and solve linear equations in one and two variables
3. Solve a variety of problems involving applications of linear and quadratic functions
4. Identify and solve quadratic equations.
5. Graph linear and non-linear relations and utilize the graph in problem solving.
6. Identifying and evaluating line slope and interpreting meaning of slope and y-intercept in the context of real world problems


MATH 416 Math for Summer Bridge 1.0 units
Description: This class is a developmental mathematics course for students new to Gavilan College who are participating in the Summer Bridge Program or other special cohorts. The purpose of the class is to review and hone basic math skills, acclimate the student to the rigors of college level work, and improve other student skills needed for learning and academic achievement. The primary mathematical focus is on prealgebra topics such as operations with whole numbers, fractions, decimals, percentage and real life problems. Students can also get practice with other topics in Algebra I such as solving linear equations, graphing linear functions, and factoring. This is a pass/no pass course. Units earned in this course do not count toward the associate degree and/or certain certificate requirements.

Student Learning Outcomes:

1. Perform basic operations with whole numbers, fractions, decimals, percentages and signed numbers without the use of a calculator
2. Develop and utilize math specific and more general study skills and test taking strategies. Measure:
3. Formulate and solve real life problems with fractions, decimals, and percentage. Measure:
4. Identify an equation as linear or quadratic and use an appropriate method to solve.
5. Analyze a linear equation in two variables, graph the equation and use the equation to solve real live applications.
6. Add, subtract, multiply, divide and factor polynomials.


MATH 430 Algebra I 5.0 units
Description: This is the first course of algebra. It will cover simplifying algebraic expressions, linear equations and inequalities, linear functions and their graphs, systems of equations, polynomials, factoring, rational expressions, and applications of all of the above. PREREQUISITE: Math 402 with a grade of "Pass", or Math 411 or Math 205A with a grade of C or better, or assessment test recommendation.

Student Learning Outcomes:

1. Simplify and evaluate algebraic expressions. Solve linear equations and inequalities in one variable including compound inequalities. Evaluate and solve formulas. Analyze and solve problems involving applications of linear equations and inequalities in one variable.
2. Graph linear functions and inequalities in two variables. Determine slope, y-intercept, x-intercept and other information from either the graph, given the equation, or other information about the line. Utilize the graphs in problem solving. Solve systems of equations and inequalities in two and three variables algebraically, Solve systems of equations in two variables graphically. Analyze and solve problems involving applications of linear equations, linear inequalities, and systems of linear equations in two variables.
3. Add/subtract, multiply and divide polynomials and numbers in scientific notation. Simplify exponential expressions using properties of exponents. Solve application problems in all of the above.
4. Identify and implement the appropriate strategy for factoring polynomials. Solve polynomial equations by factoring, set up and solve application problems involving polynomials and quadratic equations.
5. Simplify, multiply, divide, add and subtract rational expressions and solve rational equations. Simplify complex fractions. Set up and solve rational equations for application problems.
6. Analyze and translate verbal Expressions into Algebraic. Use symbolic language to name algebraic structures.
7. Demonstrate proficiency with a scientific calculator


MATH 700 Arithmetic 0.0 units
Description: This course covers arithmetic procedures with whole numbers, fractions, decimals, order of operations, ratios, proportions, percent, integers, measurements and geometry. This course may be offered in an open entry/open exit format.

Student Learning Outcomes:

1. Demonstrate proficiency with operations on whole numbers, fractions, mixed numbers, and decimals.
2. Demonstrate proficiency with ratios, proportions, percent, and operations on integers.
3. Determine and apply the appropriate methods to problems involving geometry.
4. Convert between equivalent forms of numbers and units of measurement.
5. Demonstrate problem-solving ability.