# Mathematics & Statistics

## Mathematics (MATH) Courses

### MATH 10 Developing Confidence in Math

- Units:1
- Hours:18 hours LEC
- Prerequisite:None.
- Corequisite:MATH 20, 30, 100, 110, or 120
- Catalog Date:June 1, 2021

This course helps students become more effective learners of mathematics. Topics addressed are how to overcome math anxiety and build confidence in math, study and note taking skills, time management, and test preparation.

Students must be enrolled in Math 20, 30, 100, 110 or 120 to take this course or have the permission of the instructor.

This course is graded on a Pass/No Pass basis.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- analyze causes of math anxiety.
- examine myths about learning mathematics and recognize experiences in math which have influenced personal attitudes toward math.
- create a study plan for mathematics tests and courses.
- apply learning and test-taking strategies to increase success in mathematics.

### MATH 20 Arithmetic

- Units:5
- Hours:90 hours LEC
- Prerequisite:None.
- Catalog Date:June 1, 2021

This course provides group and individual instruction in the fundamentals of arithmetic with an emphasis on written and mental computational skills. In order to enhance mental computational skills, calculators will not be allowed. Topics include operations with whole numbers, fractions, decimals, signed numbers, percents, ratios, proportions, problem solving, and applications involving measurement and geometry.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on whole numbers, fractions, and decimals.
- convert numeric information into any of the three forms: fraction, percent, decimal.
- solve computation problems involving ratios, proportions, and percents.
- solve applied problems involving whole numbers, fractions, decimals, proportions, measurement, and percents.
- convert measurement units between English and Metric using multiplication, division, and unit fractions.

### MATH 30 Pre-Algebra Mathematics

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 20 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:June 1, 2021

This course in prealgebra mathematics emphasizes the fundamental operations on integers and decimals as well as in geometric figures, measurement, and algebra with an emphasis on written and mental computational skills. Topics include: fractions; decimals; signed numbers; properties of exponents; scientific notation; evaluation of expressions and formulas; linear equations; algebraic manipulations on polynomials; and the rectangular coordinate system.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- simplify expressions with rational coefficients.
- solve linear equations in one variable involving rational numbers.
- manually solve applied problems using rational numbers, variable expressions, scientific notation, equations, geometric formulas, measurement conversions, proportions, and percent.
- graph linear equations in two variables.

### MATH 100 Elementary Algebra

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 30 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:June 1, 2021

This course includes the fundamental concepts and operations of algebra with problem solving skills emphasized throughout. Topics include: properties of real numbers, linear equations and inequalities, integer exponents, polynomials, factoring polynomials, rational expressions and equations, radical expressions and equations, systems of linear equations and inequalities, the rectangular coordinate system, graphs and equations of lines, and solving quadratic equations.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve equations involving linear, quadratic, rational and radical expressions.
- manually evaluate, simplify and expand polynomial, exponential, and rational expressions.
- completely factor polynomial expressions.
- graph solution sets of linear equations and linear inequalities in two variables.
- solve application problems using beginning context-appropriate models.

### MATH 110 Elementary Geometry

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 100 with a grade of "C" or better, or placement through the assessment process.
- General Education:AA/AS Area II(b)
- Catalog Date:June 1, 2021

This course covers aspects of elementary geometry. Topics include terms and definitions, properties of parallel lines and parallelograms, congruent and similar triangles, properties of triangles, right triangles, and basic trigonometry. Later topics include properties of circles, construction of loci, areas, and volumes. The course also emphasizes problem solving strategies, elementary logic, and reading and writing proofs. Students may be required to purchase a compass, straight edge or ruler, and a protractor.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- compute lengths, areas, and volumes of geometric objects.
- apply algebraic skills to geometric problems.
- solve mathematical and logical problems which require geometric skills.
- prove geometric theorems using both direct and indirect proof structures.
- construct geometric loci using straightedge and compass.
- utilize the appropriate trigonometric ratios to find angles and sides of right triangles.

### MATH 120 Intermediate Algebra

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 100 with a grade of "C" or better, or placement through the assessment process.
- General Education:AA/AS Area II(b)
- Catalog Date:June 1, 2021

This course reviews and extends the concepts of elementary algebra with problem solving skills emphasized throughout. Topics which are reviewed and extended include: linear and quadratic equations, factoring polynomials, rational expressions, exponents, radicals, equations of lines, and systems of equations. New topics include: larger systems of equations, absolute value equations and inequalities, rational exponents, translations and reflections of key function graphs, function notation and function operations, exponential and logarithmic functions, graphs of quadratic and simple polynomial functions, quadratic inequalities, non-linear systems of equations, and an introduction to conic sections.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve equations involving polynomial, rational, absolute value, radical, exponential, or logarithmic expressions.
- graph and recognize graphs that have undergone simple transformations (translations, reflections, and some scale factors) for linear, quadratic, exponential, logarithmic, simple rational, and simple polynomial functions.
- demonstrate the ability to appropriately use function notation, terminology, and operations.
- solve application problems using intermediate context-appropriate models.

### MATH 125 Intermediate Algebra for Statistics and Liberal Arts

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 100 with a grade of "C" or better, or placement through the assessment process.
- General Education:AA/AS Area II(b)
- Catalog Date:June 1, 2021

This course meets the prerequisite to STAT 300, Math 310, Math 300, and PSYC 330 and is intended for Liberal Arts Majors. The course topics include equations and functions that are linear, quadratic, radical, rational, exponential, and logarithmic. This course will feature discovery activities that utilize technology to help deal with applications to real data sets and problems which are current and relevant.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- identify and solve linear, radical, quadratic, rational, exponential, and logarithmic equations.
- identify and create graphs of linear, radical, quadratic, exponential, and logarithmic functions.
- construct and compare functions with their inverses.
- associate equations and information from tables or charts with their corresponding graphs.
- organize information into any/all of its four forms: words, data tables, graphs, and algebraic equations.
- accurately solve absolute value inequalities and systems of linear equations and use systems of equations to solve applied problems.
- design an accurately scaled and labeled scatterplot of data, use a best fit line to examine linear trends, interpret the meaning of slope as a rate of change.

### MATH 295 Independent Studies in Mathematics

- Units:1 - 3
- Hours:54 - 162 hours LAB
- Prerequisite:None.
- Catalog Date:June 1, 2021

### MATH 299 Experimental Offering in Mathematics

- Units:0.5 - 4
- Prerequisite:None.
- Catalog Date:June 1, 2021

### MATH 300 Introduction to Mathematical Ideas

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 120 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- Catalog Date:June 1, 2021

This course is intended for liberal arts students but may be of interest to others as well. Several specific topics will be covered including number theory, algebraic modeling, geometry, combinatorics, probability, statistics, trigonometry, graph theory, and voting and apportionment. This course is not recommended for students entering elementary school teaching or for business administration majors. A graphing calculator may be required.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- describe types of applications that would be associated with number theory and counting methods, trigonometry, geometry, statistics and algebraic modeling.
- identify appropriate procedures as well as solve applications number theory and counting methods, trigonometry, geometry, statistics, algebraic modeling, and voting and apportionment.
- apply critical thinking skills to problem solving when new types of problems are put forth.

### MATH 310 Mathematical Discovery

- Units:3
- Hours:54 hours LEC
- Prerequisite:Math 110 (Geometry) or one year of high school Geometry and Math 120 or Math 125; both with a grade of "C" or better; or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4
- Catalog Date:June 1, 2021

This course is designed to enhance students' understanding of mathematics by involving them in the mathematical process of exploration, conjecture, and proof. Students will explore mathematical patterns and relations, formulate conjectures, and prove their conjectures. Areas of mathematics from which content may be derived include number theory, statistics, probability, geometry, and sequences and series. This course is recommended for students interested in a career in education.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- explore new branches of mathematics by recognizing connections and patterns to previously encountered topics.
- solve applied problems by recognizing connections between methods of solution employed in various mathematical fields.
- develop and explain a mathematical solution to a problem not previously encountered by the student.
- explore a mathematical problem independently, extending their solution to questions not necessarily posed by the instructor.

### MATH 335 Trigonometry with College Algebra

- Units:5
- Hours:90 hours LEC
- Prerequisite:Math 120 (Intermediate Algebra) and Geometry; both with a grade of "C" or better; or placement through the assessment process.
- Transferable:CSU
- General Education:AA/AS Area II(b); CSU Area B4
- Catalog Date:June 1, 2021

This is a full trigonometry course with college algebra concepts reviewed, extended, and integrated when they are relevant to the trigonometric concepts. The trigonometric topics include right triangle trigonometry, unit circle trigonometry, graphs of trigonometric functions, proofs of trigonometric identities, solving trigonometric equations, applications of trigonometric functions (laws of sines and cosines), inverse trigonometric functions, polar coordinates, graphing polar functions, and 2-dimensional vectors. The algebra topics include exponential and logarithmic functions, complex numbers, in addition to solving equations, inequalities, and systems of equations. A graphing calculator may be required for this course.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- interpret trigonometric functions in working with right triangles, general triangles, and arcs of the unit circle.
- efficiently evaluate trigonometric and inverse trigonometric functions from memory involving special right triangles.
- efficiently evaluate trigonometric and inverse trigonometric functions at general angles from a table and by using a calculator.
- evaluate, expand, and simplify trigonometric, algebraic, logarithmic, and exponential expressions and solve equations (and prove identities) involving these expressions.
- graph and analyze trigonometric, rational, absolute value, exponential, and logarithmic functions, as well as conic sections, including algebraic transformations.
- solve application problems involving trigonometric, exponential, and logarithmic functions.

### MATH 341 Calculus for Business and Economics

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 120 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC (UC credit limitation: MATH 341, MATH 355 and MATH 400 combined: Maximum credit, one course )
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- C-ID:C-ID MATH 140
- Catalog Date:June 1, 2021

This course is designed around applications of sets, functions, limits, analytic geometry, and the differential and integral calculus in an economic and business context. This course is intended for business students; it is not recommended for mathematics and physical science majors.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- simplify algebraic expressions and solve algebraic equations related to business problems.
- evaluate limits and derivatives of algebraic, exponential and logarithmic functions, and apply them to business applications.
- formulate solutions to applications in business using definite and indefinite integrals.
- analyze functions of several variables and their relevance to business applications.

### MATH 343 Modern Business Mathematics

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 120 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU
- General Education:AA/AS Area II(b); CSU Area B4
- Catalog Date:June 1, 2021

This course is designed around applications of mathematics in an economic and business context. The major topics included are functions, finance (interest and exponential models), rates of change, optimization, and linear programming. The content of the course is structured to incorporate tables, graphs and data sets collected from real-world situations. This course is not recommended for mathematics or physical science majors. A scientific calculator will be required.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- analyze formulas, graphs, tables, and data sets in order to form conclusions and make predictions.
- calculate and interpret compound interest, present and future values, and annuities for various applications.
- graph and apply linear, quadratic, power, polynomial, exponential, and logarithmic functions in a given model.
- calculate and interpret solutions to linear programming problems.
- evaluate rates of change for a variety of functions and apply it to marginal analysis.
- calculate and interpret optimum values related to business applications.

### MATH 355 Calculus for Biology and Medicine I

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 335 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC (UC credit limitation: MATH 341, MATH 355 and MATH 400 combined: maximum credit, one course )
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- Catalog Date:June 1, 2021

This course is an introduction to differential calculus and elementary differential equations via applications in biology and medicine. It covers limits, derivatives of polynomials, trigonometric and exponential functions, graphing, and applications of the derivative to biology and medicine. Topics include the Fundamental Theorem of Calculus and techniques of integration, including integral tables and numerical methods. This course does not meet the prerequisite for the Engineering Physics series.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- differentiate polynomial, radical, trigonometric, logarithmic, and exponential functions.
- graph and analyze the curves of elementary functions.
- calculate maxima and minima of elementary functions.
- apply derivatives to applications in biology and medicine.
- integrate basic elementary functions.
- apply the Fundamental Theorem of Calculus to the evaluation of definite integrals.

### MATH 356 Calculus for Biology and Medicine II

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 355 with a grade of "C" or better
- Transferable:CSU; UC (UC credit limitation: MATH 356 and MATH 401 combined: maximum credit, one course. )
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- Catalog Date:June 1, 2021

This course covers matrix algebra with eigenvalues and eigenvectors, systems of linear equations, functions of several variables, partial derivatives, systems of differential equations, probability, and applications to biology and medicine. This course does not meet the prerequisite for the Engineering Physics series.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve systems of linear equations with matrix techniques.
- compute eigenvalues and eigenvectors for square matrices.
- solve systems of linear differential equations.
- apply systems of linear differential equations to problems in biology and medicine.
- compute partial derivatives of functions of several variables.
- compute double integrals.
- identify absolute and local extrema of functions of two variables.
- calculate equations of tangent planes to graphs of functions of two variables.

### MATH 370 Pre-Calculus Mathematics

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 335 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- Catalog Date:June 1, 2021

This course is designed to prepare students for Calculus for STEM majors. Course content includes a brief review followed by an in-depth extension of the properties of polynomial, rational, exponential, logarithmic and trigonometric functions. Additional topics include systems of linear and non-linear equations and inequalities, conic sections, sequences and series, binomial theorem, analytic geometry, vectors, parametric, and polar equations. A graphing calculator may be required for this course.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve equations/inequalities involving polynomial, logarithmic, and exponential expressions.
- solve equations/inequalities involving trigonometric expressions. All students must be able to efficiently evaluate trigonometric functions using memorized special right triangle facts but tables of information and/or calculators may be used on application problems.
- graph and analyze polynomial, rational, absolute value, radical, exponential, logarithmic, and trigonometric functions using algebraic transformations.
- apply the properties of vectors, matrices, sequences, series, the polar coordinate system, and the binomial theorem to calculus or science problems.
- prove mathematical facts using algebraic manipulation, fundamental trigonometric identities, direct proof, indirect proof, and the principle of mathematical induction.
- solve applied problems using functions, vectors, matrices, sequences and series.

### MATH 400 Calculus I

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 370 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC (UC credit limitation: MATH 341, MATH 355 and MATH 400 combined: maximum credit, one course )
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- C-ID:C-ID MATH 210
- Catalog Date:June 1, 2021

This course explores the basic concepts of analytic geometry, limits of functions, derivatives, and integrals. Topics covered will include finding the limits of functions by graphing and indeterminate forms of algebraic expressions. Derivatives and integrals involving algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions will also be covered. Many applications will be covered, including those involving rectilinear motion, differentials, related rates, graphing, optimization, and finding areas of bounded regions. A graphing calculator may be required for this course.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- calculate limits and derivatives of algebraic and transcendental functions using a variety of techniques.
- demonstrate a knowledge of basic facts and formulas with limits, derivatives, and integration.
- graph algebraic and transcendental functions using information from limits, continuity, and derivatives.
- solve problems using derivatives including equations of tangent lines, related rates applications and optimization application problems.
- apply both the limit process and the Fundamental Theorem of Calculus to evaluate area related problems and utilize the appropriate substitution techniques to evaluate integrals.
- prove calculus theorems related to limits and derivatives.

### MATH 401 Calculus II

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 400 with a grade of "C" or better
- Transferable:CSU; UC (UC credit limitation: MATH 356 and MATH 401 combined: maximum credit, one course )
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- C-ID:C-ID MATH 220
- Catalog Date:June 1, 2021

This course is a continuation of MATH 400. Topics covered include techniques of integration, numerical integration, improper integrals, infinite series, parametric equations, polar coordinates, and conic sections. Many applications will be covered including those involving areas between plane regions, volumes of revolution, work, moments and concepts of mass, average value, arc length, and surface area. A graphing calculator may be required for this course.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- utilize a variety of algebraic and trigonometric techniques to evaluate integral expressions.
- apply integration to problems involving volume, centers of mass, and work.
- analyze and manipulate infinite series, Taylor polynomials, and functions represented by power series.
- apply differentiation and integration techniques to equations in parametric and polar form.
- prove selected calculus theorems related to first year calculus.

### MATH 402 Calculus III

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 401 with a grade of "C" or better
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- C-ID:C-ID MATH 230
- Catalog Date:June 1, 2021

This course extends the concepts of limits, derivatives and integrals to vector-valued functions and functions of more than one variable. Topics covered will include three-dimensional analytic geometry and vectors, partial derivatives, multiple integrals, line integrals, surface integrals, and the theorems of Green, Gauss (Divergence), and Stokes. Many applications of the calculus will be included. A graphing calculator may be required for this course.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- compute a number of vector based function values on plane curves and space curves. These include velocity vectors, acceleration vectors, speed, curvature, arc-length, binormal vectors, unit tangent and unit normal vectors.
- optimize both a multivariate function of a surface and multivariate functions involving a constraint curve.
- utilize multiple integrals using rectangular, polar, cylindrical, or spherical coordinates in problems involving volume, moments, and mass.
- set up and evaluate line and surface integrals.
- apply Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem to physics and engineering applications.

### MATH 410 Introduction to Linear Algebra

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 401 with a grade of "C" or better
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4
- C-ID:C-ID MATH 250
- Catalog Date:June 1, 2021

This course introduces linear algebra. Topics include matrices, determinants, systems of equations, vector spaces, linear transformations, eigenvectors, and applications. This course is intended for majors in mathematics, engineering, science, and related fields.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve a variety of systems of equations using matrices using 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.
- 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.

### MATH 420 Differential Equations

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 401 with a grade of "C" or better
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4
- C-ID:C-ID MATH 240
- Catalog Date:June 1, 2021

This course is a study of ordinary differential equations, including linear equations, systems of equations, equations with variable coefficients, existence and uniqueness of solutions, series solutions, singular points, transform methods, boundary value problems, and applications.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve a variety of ordinary differential equations using techniques such as reduction of order, method of undetermined coefficients, variation of parameters, power series, and Laplace transforms.
- analyze, model, and solve elementary applied science problems such as Newton's Law of Cooling, mixing, falling bodies, and Newton's Second Law of Motion with ordinary differential equations.
- identify differential equations such as linear, separable, exact, and Cauchy-Euler.
- solve systems of linear differential equations.
- evaluate ordinary differential equations for existence and uniqueness of solutions using appropriate theorems.

### MATH 495 Independent Studies in Mathematics

- Units:1 - 3
- Hours:54 - 162 hours LAB
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:June 1, 2021

### MATH 499 Experimental Offering in Mathematics

- Units:0.5 - 4
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:June 1, 2021

## Mathematics Support (MATHS) Courses

### MATHS 15 Support for Intermediate Algebra

- Units:3
- Hours:54 hours LEC
- Prerequisite:None.
- Corequisite:MATH 120
- Catalog Date:June 1, 2021

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 120, Intermediate Algebra. You must be enrolled in the corresponding section of Math 120 while taking this course. Topics and homework assignments are often connected to the students' assignments in MATH 120. This class is graded on a pass/no pass basis and does not meet math competency.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to simplify expressions and solve equations involving absolute values, polynomials, rational expressions, radicals, exponentials, and logarithms.
- use support mathematics skills to solve systems of equations and solve linear, polynomial, and absolute value inequalities.
- use support mathematics skills to demonstrate an understanding of the definition of a function and use function notation, including the algebra of functions, composite functions, and inverse functions.
- use support mathematics skills to sketch the graphs of basic functions and the transformations of these functions.
- use support mathematics skills to apply algebraic methods when solving word problems.

### MATHS 46 Support for Calculus for Business and Economics

- Units:3
- Hours:54 hours LEC
- Prerequisite:None.
- Corequisite:MATH 341
- Catalog Date:June 1, 2021

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Math 341, Calculus for Business and Economics. You must be enrolled in the corresponding section of Math 341 while taking this course. Topics and homework assignments are often connected to the students' assignments in MATH 341. The course includes applications of the concepts and skills covered. This class is graded on a pass/no pass basis and does not meet math competency. A scientific calculator will be required for this course.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to find the derivatives of polynomial, rational, exponential, and logarithmic functions.
- use support mathematics skills to find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule.
- use support mathematics skills to sketch the graphs of functions using horizontal and vertical asymptotes, intercepts, 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.
- use support mathematics skills to analyze the marginal cost, profit, and revenue when given the appropriate function.
- use support mathematics skills to determine maxima and minima in optimization problems using the derivative.
- use support mathematics skills to find rates of change and tangent lines.
- use support mathematics skills to analyze revenue, cost, and profit.
- use support mathematics skills to find definite and indefinite integrals when applying the general integral formulas, integration by substitution, and other integration techniques.
- use support mathematics skills in business and economics applications.

### MATHS 55 Support for Trigonometry with College Algebra

- Units:3
- Hours:54 hours LEC
- Prerequisite:None.
- Corequisite:MATH 335
- Catalog Date:June 1, 2021

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 335: Trigonometry with College Algebra. You must be enrolled in the corresponding section of Math 335 while taking this course. Topics and homework assignments are often connected to the students' assignments in MATH 335. The course includes applications of the concepts and skills covered. A scientific calculator is required for this course. See notes on the e-schedule for more information. This class is graded on a pass/no pass basis and does not meet math competency.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to apply trigonometric functions to the angles of a right triangle and arcs on the unit circle.
- use support mathematics skills to evaluate trigonometric functions of common angles (using both radian and degree measure) and inverse trigonometric functions.
- use support mathematics skills to recognize, apply, and prove trigonometric identities and solve trigonometric equations.
- use support mathematics skills to create and analyze graphs of polynomial functions, rational functions, trigonometric functions, inverse trigonometric functions, curves in parametric form, and curves in polar form. (Trigonometric function graphing will include changes in period, phase, and amplitude.)
- use support mathematics skills to convert between polar and rectangular coordinates and equations, compute and solve equations involving complex numbers in standard and trigonometric form, and use DeMoivre's Theorem to evaluate powers and roots of complex numbers.
- use support mathematics skills to apply trigonometric and algebraic concepts as problem-solving tools by modeling problems with appropriate equations, including use of the Laws of Sines and Cosines and vector applications with vectors represented in both (a, b) and ai+bj form.

### MATHS 80 Calculus I: Problem Solving

- Units:1
- Hours:18 hours LEC
- Prerequisite:None.
- Corequisite:MATH 400
- Catalog Date:June 1, 2021

This course provides additional problem solving practice, theory practice, and study skills support for students concurrently enrolled in MATH 400, Calculus I. Please refer to the class notes in the online schedule of classes for details to the particular sections of MATH 400 that will be associated with this section. This class is graded on a pass/no pass basis and does not meet math competency. A graphing calculator may be required.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- calculate limits and derivatives of algebraic and transcendental functions using a variety of techniques.
- graph algebraic and transcendental functions using information from limits, continuity, and derivatives.
- solve problems using derivatives including equations of tangent lines, related rates applications and optimization application problems.
- apply both the limit process and the Fundamental Theorem of Calculus to evaluate area related problems and utilize the appropriate substitution techniques to evaluate integrals.

### MATHS 81 Calculus II: Problem Solving

- Units:1
- Hours:18 hours LEC
- Prerequisite:None.
- Corequisite:MATH 401
- Catalog Date:June 1, 2021

This course provides additional problem solving practice, theory practice, and study skills support for students concurrently enrolled in MATH 401, Calculus II. Please refer to the class notes in the online schedule of classes for details to the particular sections of MATH 401 that will be associated with this section. This class is graded on a pass/no pass basis and does not meet math competency. A graphing calculator may be required.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use integrals to define volumes of regions of revolution about horizontal and vertical lines, arc-length, area of surfaces of revolution, calculations of work, moments, and mass.
- apply a number of different integration techniques to evaluate integrals. These include integration by parts, trigonometric substitution, and partial fraction decomposition.
- utilize differentiation and integration, and some of their basic applications within parametric equations and polar equations.
- create Taylor Polynomials to approximate functions and manipulate these using algebraic or calculus techniques to model additional functions.

### MATHS 82 Calculus III: Problem Solving

- Units:1
- Hours:18 hours LEC
- Prerequisite:None.
- Corequisite:MATH 402
- Catalog Date:June 1, 2021

This course provides additional problem solving practice, theory practice, and study skills support for students concurrently enrolled in MATH 402, Calculus III. Please refer to the class notes in the online schedule of classes for details to the particular sections of MATH 402 that will be associated with this section. This class is graded on a pass/no pass basis and does not meet math competency. A graphing calculator may be required.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- compute a number of vector based function values on plane curves and space curves. These include velocity vectors, acceleration vectors, speed, curvature, arc-length, binormal vectors, unit tangent and unit normal vectors.
- optimize both a multivariate function of a surface and multivariate functions involving a constraint curve.
- utilize multiple integrals using rectangular, polar, cylindrical, or spherical coordinates in problems involving volume, moments, and mass.
- set up and evaluate line and surface integrals.
- apply Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem to physics and engineering applications.

### MATHS 95 Support for Introduction to Mathematical Ideas

- Units:2
- Hours:36 hours LEC
- Prerequisite:None.
- Corequisite:MATH 300
- Catalog Date:June 1, 2021

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Math 300, Introduction to Mathematical Ideas. You must be enrolled in the corresponding section of Math 300 while taking this course. Topics and homework assignments are often related to the students' assignments in MATH 300. The course includes applications of the concepts and skills covered. This class is graded on a pass/no pass basis and does not meet math competency. A scientific calculator may be required for this course.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to describe types of applications that would be associated with number theory and counting methods, trigonometry, geometry, statistics and algebraic modeling.
- use support mathematics skills to identify appropriate procedures as well as solve applications in number theory and counting methods, trigonometry, geometry, statistics, algebraic modeling, and voting and apportionment.
- use support mathematics skills to apply critical thinking skills to problem solving when new types of problems are put forth.

### MATHS 299 Experimental Offering in Mathematics Support

- Units:0.5 - 4
- Prerequisite:None.
- Catalog Date:June 1, 2021

### MATHS 499 Experimental Offering in Mathematics Support

- Units:0.5 - 4
- Prerequisite:None.
- Catalog Date:June 1, 2021

## Statistics (STAT) Courses

### STAT 10 Support for Introduction to Probability and Statistics

- Units:2
- Hours:36 hours LEC
- Prerequisite:None.
- Corequisite:STAT 300
- Catalog Date:June 1, 2021

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in STAT 300, Introduction to Probability and Statistics. You must be enrolled in the corresponding section of STAT 300 while taking this course. Topics and homework assignments are often connected to the students' assignments in STAT 300. The course includes applications of the concepts and skills covered. Students will be expected to use technology for data analysis. Appropriate technology includes at least one of the following: TI-Graphing calculator, StatCrunch, Excel, SPSS or Minitab. See class notes in the e-schedule for more information. This class is graded on a pass/no pass basis and does not meet math competency.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- demonstrate relevant arithmetic and algebraic skills and interpret results in the context of the data or scenario in the context of using statistical formulas and methods.
- compute and explain simple probabilities and use geometric reasoning to find probabilities based on area under a normal curve.
- implement study habits that promote success in statistics, such as the use of reading and metacognitive strategies to improve understanding and performance.

### STAT 101 Pre-Statistics

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 100 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:June 1, 2021

This course will satisfy the prerequisite to STAT 300. Topics include ratios, rates, and proportional reasoning; arithmetic with fractions, decimals and percents; evaluating expressions, solving equations, and analyzing formulas to understand statistical measures; use of linear and exponential functions to model bivariate data; graphical and numerical descriptive statistics for quantitative and categorical data. Note: This course is not intended for students who plan to take courses in science, computer information science, engineering, mathematics, physics, chemistry, or business related majors. A scientific or graphing calculator with 2-variable statistics capabilities is required.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- simplify linear expressions, solve linear equations and inequalities, and evaluate statistical formulas using the order of operations agreement.
- sketch the graphs of linear and exponential functions, and find equations of linear and exponential functions given two points on the line or curve.
- apply and interpret algebraic and statistical models when solving word problems.

### STAT 300 Introduction to Probability and Statistics

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 120 or 125 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC (UC credit limitation: 330 and STAT 300 combined: maximum credit, one course)
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- C-ID:C-ID MATH 110
- Catalog Date:June 1, 2021

This course is an introduction to probability and statistics. Topics include: elementary principles and applications of descriptive statistics, elementary probability principles, probability distributions, estimation of parameters, hypothesis testing, linear regression and correlation, and ANOVA. Statistical analysis using a computer statistics package or graphing calculator will be required.

#### Student Learning Outcomes

Upon completion of this course, the student 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 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 analyse 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.
- 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.

### STAT 495 Independent Studies in Statistics

- Units:1 - 3
- Hours:54 - 162 hours LAB
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:June 1, 2021

### STAT 499 Experimental Offering in Statistics

- Units:0.5 - 4
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:June 1, 2021

(See catalog p. 21)

## Science, Technology, Engineering, and Mathematics

This program is part of the Science, Technology, Engineering, and Mathematics meta-major.