Mathematics and Statistics
Overview
ARC offers mathematics and statistics courses to meet the educational goals of all our students, which include personal enrichment, associate degrees, certificates, and transferring to a university. Some of our courses serve a wide range of academic goals, such as Math 333: Introduction to College Algebra, while other courses are geared toward specific goals, such as Math 340: Calculus for Business and Economics. In a datadriven culture, we help students understand some of the ways in which mathematics and statistics can be used in the world around us.
Our mathematics and statistics faculty come from a wide variety of backgrounds and are proud of the variety of ways we support our students. Our courses are offered in a variety of modalities, such as facetoface, online, and hybrid. We also have a Math Learning Center that enables students to work independently on some courses under the guidance of a faculty member with tutorial support. Many of our courses are linked with a concurrent support course so that students have an opportunity to strengthen the skills needed for success in the transferlevel course. Our thriving MESA program supports students majoring in STEM, especially firstgeneration college students. Students can find community and a variety of opportunities in their HomeBase.
Please note: In compliance with CA Legislation AB 705 and AB 1705, pretransferlevel courses (those numbered below 300, for example Math 120) are no longer being offered.
Roadmaps
Road maps lay out all of the courses you need to take for a given degree or certificate.
A.A./A.S. Degrees
AAT/AST Transfer Degrees
 Dean (Interim) Michelle Brock

Department Chairs
Matt Mitchell
Amy Gaudard  HomeBase STEM HomeBase
 Phone (916) 4848215
 Email askhbSTEM@arc.losrios.edu
Associate Degrees for Transfer
A.S.T. in Mathematics
This degree is designed to meet common lowerdivision requirements for a major in Mathematics at a CSU campus. Satisfactory completion of the ARC Mathematics transfer degree provides a solid foundation and satisfies the standard prerequisites for upper division coursework for Mathematics majors. However, it is highly recommended that students meet with a counselor since major and general education requirements vary for each college/university.
The Mathematics Associate in Science for Transfer (AST) Degree may be obtained by the completion of 60 transferable, semester units with a minimum 2.0 GPA, including (a) the major or area of emphasis described in the Required Program outlined below (earning a C or better in these courses) and (b) either the Intersegmental General Education Transfer Curriculum (IGETC) or the California State University General Education Breadth Requirements.
Catalog Date: August 1, 2024
Degree Requirements
Course Code  Course Title  Units 

MATH 400  Calculus I (5)  5 
MATH 401  Calculus II (5)  5 
MATH 402  Calculus III (5)  5 
MATH 410  Introduction to Linear Algebra (3)  3 
MATH 420  Differential Equations (4)  4 
Total Units:  22 
The Associate in Science in Mathematics for Transfer (AST) degree may be obtained by completion of 60 transferable, semester units with a minimum overall grade point average (GPA) of 2.0, including (a) a minimum grade of "C" (or "P") for each course in the major or area of emphasis described in the Required Program, and (b) either the Intersegmental General Education Transfer Curriculum (IGETC) or the California State University General EducationBreadth Requirements.
Student Learning Outcomes
Upon completion of this program, the student will be able to:
 evaluate, describe, and apply single variable calculus including various forms of derivatives and integrals, to analyze and solve problems.
 evaluate, describe, and apply multivariate calculus, linear algebra, and differential equations to analyze and solve problems.
 prepare logical arguments and use them to prove basic mathematical theorems.
 solve realworld application problems using appropriate mathematical problemsolving skills.
Career Information
Mathematicians work as statisticians, analysts, computer programmers, actuaries, researchers, planners, and educators. This transfer degree is designed to meet the common lowerdivision requirements for most bachelor's degrees in Mathematics.
Associate Degrees
A.S. in Mathematics
This degree provides a mathematical foundation for students preparing to transfer to a fouryear program in mathematics or statistics. Coursework includes a threesemester calculus series, differential equations, linear algebra, and statistics and/or symbolic logic.
Catalog Date: August 1, 2024
Degree Requirements
Course Code  Course Title  Units 

MATH 400  Calculus I  5 
MATH 401  Calculus II  5 
MATH 402  Calculus III  5 
MATH 410  Introduction to Linear Algebra  3 
MATH 420  Differential Equations  4 
A minimum of 3 units from the following:  3  
MATH 320  Symbolic Logic (3)  
or PHIL 324  Symbolic Logic (3)  
STAT 300  Introduction to Probability and Statistics (4)  
or STAT 480  Introduction to Probability and Statistics  Honors (4)  
Total Units:  25 
The Mathematics Associate in Science (A.S.) degree may be obtained by completion of the required program, plus general education requirements, plus sufficient electives to meet a 60unit total. See ARC graduation requirements.
Student Learning Outcomes
Upon completion of this program, the student will be able to:
 identify, formulate, and solve applied problems (using calculus and linear algebra) in verbal, numeric, graphical, and symbolic form related to science, economics, or business.
 recognize and construct valid arguments using deductive and inductive reasoning skills.
 define and utilize terminology of mathematics with emphasis in calculus, linear algebra, and either statistics, logic, or problem solving.
 calculate derivatives and integrals using a variety of defined rules and strategies of calculus, algebraic properties and trigonometric identities.
A.S. in Physical Science/Mathematics
This degree provides a broad study in the fields of physical science and mathematics. It prepares for transfer to a fouryear program in science, technology, engineering, or mathematics (STEM).
Catalog Date: August 1, 2024
Degree Requirements
Course Code  Course Title  Units 

A minimum of 18 units from the following:  18  
ASTR 300  Introduction to Astronomy (3)  
ASTR 310  The Solar System (3)  
ASTR 320  Stars, Galaxies, and Cosmology (3)  
ASTR 330  Introduction to Astrobiology (3)  
ASTR 400  Astronomy Laboratory (1)  
ASTR 481  Honors Astronomy: Stars, Galaxies, and Cosmology (4)  
ASTR 495  Independent Studies in Astronomy (1  3)  
ASTR 499  Experimental Offering in Astronomy (0.5  4)  
CHEM 305  Introduction to Chemistry (5)  
CHEM 306  Introduction to Organic and Biological Chemistry (5)  
CHEM 309  Integrated General, Organic, and Biological Chemistry (5)  
CHEM 310  Chemical Calculations (4)  
CHEM 338  Chemistry In Your World (3)  
CHEM 400  General Chemistry I (5)  
CHEM 401  General Chemistry II (5)  
CHEM 420  Organic Chemistry I (5)  
CHEM 421  Organic Chemistry II (5)  
CHEM 423  Organic Chemistry  Short Survey (5)  
CHEM 495  Independent Studies in Chemistry (1  3)  
CHEM 499  Experimental Offering in Chemistry (0.5  4)  
ENGR 300  Introduction to Engineering (1)  
ENGR 310  Engineering Survey Measurements (4)  
ENGR 312  Engineering Graphics (3)  
ENGR 401  Introduction to Electrical Circuits and Devices (4)  
ENGR 412  Properties of Materials (4)  
ENGR 420  Statics (3)  
ENGR 495  Independent Studies in Engineering (1  3)  
ENGR 499  Experimental Offering in Engineering (0.5  4)  
GEOG 300  Physical Geography: Exploring Earth's Environmental Systems (3)  
GEOG 301  Physical Geography Laboratory (1)  
GEOG 305  Global Climate Change (3)  
GEOG 306  Weather and Climate (3)  
GEOG 307  Environmental Hazards and Natural Disasters (3)  
GEOG 308  Introduction to Oceanography (3)  
GEOG 309  Introduction to Oceanography Lab (1)  
GEOG 391  Field Studies in Geography: Mountain Landscapes (1  4)  
GEOG 392  Field Studies in Geography: Coastal Landscapes (1  4)  
GEOG 393  Field Studies in Geography: Arid Landscapes (1  4)  
GEOG 394  Field Studies in Geography: Volcanic Landscapes (1  4)  
GEOG 495  Independent Studies in Geography (1  3)  
GEOG 499  Experimental Offering in Geography (0.5  4)  
GEOL 300  Physical Geology (3)  
GEOL 301  Physical Geology Laboratory (1)  
GEOL 305  Earth Science (3)  
GEOL 306  Earth Science Laboratory (1)  
GEOL 310  Historical Geology (3)  
GEOL 311  Historical Geology Laboratory (1)  
GEOL 320  Global Climate Change (3)  
GEOL 325  Environmental Hazards and Natural Disasters (3)  
GEOL 330  Introduction to Oceanography (3)  
GEOL 331  Introduction to Oceanography Lab (1)  
GEOL 345  Geology of California (3)  
GEOL 392  Field Studies in Mountain Landscapes (1  4)  
GEOL 393  Field Studies in Coastal Landscapes (1  4)  
GEOL 394  Field Studies in Volcanic Landscapes (1  4)  
GEOL 495  Independent Studies in Geology (1  3)  
GEOL 499  Experimental Offering in Geology (0.5  4)  
MATH 300  Introduction to Mathematical Ideas (3)  
MATH 310  Mathematical Discovery (3)  
MATH 311  Mathematical Concepts for Elementary School Teachers  Number Systems (3)  
MATH 320  Symbolic Logic (3)  
or PHIL 324  Symbolic Logic (3)  
MATH 333  Introduction to College Algebra (3)  
MATH 340  Calculus for Business and Economics (3)  
MATH 342  Modern Business Mathematics (3)  
MATH 355  Calculus for Biology and Medicine I (4)  
MATH 356  Calculus for Biology and Medicine II (4)  
MATH 372  College Algebra for Calculus (4)  
MATH 373  Trigonometry for Calculus (4)  
MATH 375  PreCalculus (6)  
MATH 400  Calculus I (5)  
MATH 401  Calculus II (5)  
MATH 402  Calculus III (5)  
MATH 410  Introduction to Linear Algebra (3)  
MATH 420  Differential Equations (4)  
MATH 480  Honors Seminar in Mathematics (1)  
MATH 495  Independent Studies in Mathematics (1  3)  
MATH 499  Experimental Offering in Mathematics (0.5  4)  
PHYS 310  Conceptual Physics (3)  
PHYS 311  Basic Physics (3)  
PHYS 312  Conceptual Physics Laboratory (1)  
PHYS 350  General Physics (4)  
PHYS 360  General Physics (4)  
PHYS 410  Mechanics of Solids and Fluids (5)  
PHYS 421  Electricity and Magnetism (4)  
PHYS 431  Heat, Waves, Light and Modern Physics (4)  
PHYS 495  Independent Studies in Physics (1  3)  
PHYS 499  Experimental Offering in Physics (0.5  4)  
STAT 300  Introduction to Probability and Statistics (4)  
STAT 305  Statway, Part II (6)  
STAT 480  Introduction to Probability and Statistics  Honors (4)  
STAT 495  Independent Studies in Statistics (1  3)  
STAT 499  Experimental Offering in Statistics (0.5  4)  
Total Units:  18 
The Physical Science/Mathematics Associate in Science (A.S.) degree may be obtained by completion of the required program, plus general education requirements, plus sufficient electives to meet a 60unit total. See ARC graduation requirements.
Student Learning Outcomes
Upon completion of this program, the student will be able to:
 recognize and correctly use the terminology of math, statistics, and/or science.
 analyze and interpret data, charts, and graphs using quantitative and qualitative methods.
 recognize and construct valid arguments using deductive and inductive reasoning.
 evaluate new and accepted ideas about the natural universe using testable methodology.
Mathematics (MATH) Courses
MATH 10 Developing Confidence in Math
 Units:1
 Hours:18 hours LEC
 Prerequisite:None.
 Advisory:Concurrent enrollment in another math course
 Catalog Date:August 1, 2024
This course helps students recognize common misconceptions of mathematics, overcome math anxiety, and build confidence in math. Topics include relaxation techniques, study habits, and problem solving strategies. This course is also useful for tutors, counselors, and teachers interested in helping others overcome their math anxiety. Pass/No Pass only.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 analyze causes of math anxiety.
 examine myths about mathematics.
 describe the experiences in mathematics which have influenced personal attitudes towards math.
 compare personal learning experiences, as related to mathematics.
 apply skills to overcome fear and achieve success in mathematics.
 create a study plan for mathematics courses.
 apply learning strategies to achieve success in mathematics.
MATH 25 Computational Arithmetic
 Units:3
 Hours:54 hours LEC
 Prerequisite:None.
 Catalog Date:August 1, 2024
This course introduces the fundamentals of arithmetic with an emphasis on computational skills. Topics include whole numbers, exponents, order of operations, factors, fractions, decimals, problem solving, and applications.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 evaluate problems using addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals.
 use the order of operations to simplify expressions.
 read, write, and round whole numbers and decimals.
 identify and use factors and prime factorization of whole numbers.
 identify types of fractions.
 simplify fractions.
 demonstrate the relationships between fractions and decimals.
 set up and solve application problems using computational arithmetic.
MATH 32 PreAlgebra
 Units:3
 Hours:54 hours LEC
 Prerequisite:Through the Los Rios Placement Process or successful completion of Arithmetic.
 Catalog Date:August 1, 2024
This course briefly reviews the fundamentals of arithmetic, including fractions, decimals, and order of operations. Course content includes signed numbers, ratios, proportions, percent, concepts of variables, area/perimeter/volume of geometric figures, and solving basic linear equations.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 evaluate numerical expressions that contain integers, fractions, and decimals using the order of operations.
 evaluate algebraic expressions for given value(s) of the variable(s).
 simplify variable expressions by using the distributive property and combining similar terms.
 solve elementary linear equations.
 set up and solve elementary application problems, including problems involving percents, ratios, and proportions.
 convert between percents, decimals, and fractions.
 convert units of measurement, including U.S. and metric systems.
 evaluate numerical square root expressions.
 calculate area, perimeter, and volume of geometric figures.
MATH 41 Algebra Readiness  Part I
 Units:3
 Hours:54 hours LEC
 Prerequisite:None.
 Advisory:CISC 100, CISC 300, or CISC 305 with a grade of "C" or better, AND ENGRD 116 or ESLR 320 with a grade of "C" or better. Placement through the math assessment process.
 Catalog Date:August 1, 2024
This course is the first of two parts covering algebra readiness in a masterybased learning environment. It introduces the fundamentals of arithmetic, and emphasizes problem solving and computational skills. Topics include whole numbers, exponents, order of operations, factors, fractions, decimals, proportion, ratios, rates, problem solving, and applications. Students who complete this course during the first half of the semester may sign up immediately for MATH 42. For the most updated information, please visit the Math Learning Center (MLC) web page on the ARC website. Completion of MATH 41 with a grade of "C" or better meets the prerequisite for MATH 42 and MATH 32.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 evaluate problems using addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals, without the use of a calculator.
 use the order of operations to simplify expressions without the use of a calculator.
 read, write, and round whole numbers and decimals.
 identify and use factors and prime factorizations of whole numbers.
 analyze and simplify fractions without the use of a calculator.
 demonstrate the relationships between fractions, decimals, and percents.
 analyze and estimate problems involving whole numbers, fractions, and decimals.
 set up and solve application problems using computational arithmetic without the use of a calculator.
MATH 42 Algebra Readiness  Part II
 Units:3
 Hours:54 hours LEC
 Prerequisite:Through the Los Rios Placement Process.
 Catalog Date:August 1, 2024
This course is the second of two parts covering algebra readiness in a masterybased learning environment. It introduces the fundamentals of prealgebra, with an emphasis on problem solving skills. Topics include order of operations, signed numbers, application problems, concepts of variables, exponents, operations on signed fractions, percent problems, solving algebraic equations, the rectangular coordinate system, introduction to graphing linear equations, applications of equations, and area/perimeter of geometric figures. Students who complete this course during the first half of the semester may sign up immediately for MATH 131. For the most updated information, please visit the MMLC web page on the ARC website. Completion of MATH 41 AND MATH 42 with grades of "C" or better meets the prerequisite for MATH 131, MATH 100, MATH 129, and STAT 105.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 evaluate expressions that contain addition, subtraction, multiplication, and division of real numbers without the use of a calculator.
 solve numerical and applied percent problems.
 simplify algebraic expressions using order of operations without the use of a calculator.
 evaluate and simplify exponential and square root expressions.
 solve linear equations, including those with signed numbers, fractions, and/or decimals without the use of a calculator.
 set up and solve elementary application problems using algebraic techniques without the use of a calculator.
 compute perimeter and area of geometric figures.
 translate words into symbols and equations without the use of a calculator.
 perform operations on signed fractions without the use of a calculator.
 graph linear equations without the use of a calculator.
MATH 100 Elementary Algebra
 Units:5
 Hours:90 hours LEC
 Prerequisite:Through the Los Rios Placement Process or successful completion of Prealgebra.
 Catalog Date:August 1, 2024
This course covers the fundamental concepts and operations of algebra and incorporates problemsolving skills. Topics include properties of real numbers, linear equations and inequalities, integer exponents, polynomials, and factoring polynomials. Other topics include rational and radical expressions, rational and radical equations, graphing and finding equations of lines, graphing and solving systems of linear equations, and graphing and solving quadratic equations.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 simplify expressions using the basic operations and properties of real numbers.
 solve onevariable equations and inequalities.
 combine polynomials using the basic operations of polynomials.
 factor polynomials.
 simplify rational expressions.
 solve rational equations.
 solve linear equations.
 graph linear equations.
 find the equation of a line given (a) the slope and a point on the line, and (b) two points on the line.
 solve and graph systems of linear equations.
 simplify expressions containing integer exponents.
 simplify expressions containing second and third degree roots.
 solve quadratic equations.
 graph quadratic equations.
 develop an appropriate equation or system of equations and use the resulting equation(s) to solve application problems.
MATH 110 Elementary Geometry
 Units:5
 Hours:90 hours LEC
 Prerequisite:Through the Los Rios Placement Process or successful completion of Algebra I/Integrated Math 1 or Beginning Algebra.
 Catalog Date:August 1, 2024
This course covers aspects of elementary geometry. Topics include geometric terms and definitions, properties of parallel lines and parallelograms, congruent and similar triangles, properties of triangles, right triangles, basic trigonometry, properties of circles, geometric constructions, areas, and volumes. The course also emphasizes problemsolving strategies, elementary logic, and writing proofs.
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 direct proof structures.
 construct geometric loci using a straightedge and compass.
 select the appropriate trigonometric identity to find angles and sides of right triangles.
 identify theorems that relate angles, arcs, intercepted arcs in circles and polygons.
MATH 120 Intermediate Algebra
 Units:5
 Hours:90 hours LEC
 Prerequisite:Through the Los Rios Placement Process or successful completion of Algebra I/Integrated Math 1 or Beginning Algebra.
 General Education:AA/AS Area II(b)
 Catalog Date:August 1, 2024
This course extends and reviews the concepts of elementary algebra while incorporating applications and problemsolving skills. Reviewed and extended topics include linear and quadratic equations and their graphs, linear inequalities, systems of linear equations, exponents, factoring polynomials, rational expressions, and radicals. New topics include absolute value equations and inequalities, graphs of absolute value functions, equations of parallel and perpendicular lines, graphs of linear inequalities, graphs of systems of linear inequalities, functions, function notation, domain and range, inverse functions, exponential and logarithmic functions and their graphs, quadratic and polynomial functions and their graphs, an introduction to the complex number system, finding the real and complex solutions for a variety of equations, an introduction to conic sections, and nonlinear systems of equations and their graphs.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 graph and solve linear inequalities.
 graph systems of linear inequalities.
 solve equations and inequalities containing absolute values.
 solve and graph linear equations and systems of linear equations.
 create linear equations that pass through a given point and are parallel to a given line.
 create linear equations that pass through a given point and are perpendicular to a given line.
 simplify polynomial expressions.
 choose and apply appropriate techniques to factor a variety of polynomials.
 state whether a mathematical relation is a function and find its domain and range.
 construct the inverse of a given function.
 sketch graphs of basic exponential functions.
 utilize the properties of exponents to simplify exponential expressions and to solve exponential equations.
 sketch graphs of basic logarithmic functions.
 utilize the properties of logarithms to simplify logarithmic expressions and to solve logarithmic equations.
 simplify expressions containing radicals, using complex numbers where appropriate.
 solve quadratic equations for real and complex solutions.
 solve equations containing radicals.
 simplify rational expressions and solve rational equations for real and complex solutions.
 sketch graphs of basic conic sections.
 solve and graph systems of nonlinear equations.
 develop an appropriate equation or system of equations and use the resulting equation(s) to solve application problems.
MATH 125 Intermediate Algebra for Statistics and Liberal Arts
 Units:4
 Hours:72 hours LEC
 Prerequisite:Through the Los Rios Placement Process or successful completion of Algebra I/Integrated Math 1 or Beginning Algebra.
 General Education:AA/AS Area II(b)
 Catalog Date:August 1, 2024
This is an intermediate algebra course for nonSTEM students. Topics include linear functions, models, systems, and graphs, as well as polynomial, exponential, logarithmic, and quadratic functions. The course emphasizes authentic applications and mathematical models using realworld data. This course does not meet the prerequisite for STEMtrack math courses.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 identify and solve various types of equations and systems of equations.
 factor a variety of polynomials.
 collect like terms in simplifying polynomial, exponential, and logarithmic functions.
 create graphs of lines, parabolas, exponential, and logarithmic functions.
 associate equations and information from tables or charts with their corresponding graphs.
 explain the concept of a mathematical function/relation and use functional notation appropriately to formulate solutions.
 construct and compare inverse functions with their original functions.
 explain what a logarithm is and solve logarithmic equations and applications.
MATH 129 Elementary and Intermediate Algebra
 Units:9
 Hours:162 hours LEC
 Prerequisite:Through the Los Rios Placement Process or successful completion of Prealgebra.
 General Education:AA/AS Area II(b)
 Catalog Date:August 1, 2024
This course covers the concepts of elementary and intermediate algebra with an emphasis on problem solving. Topics include linear and quadratic equations, inequalities, factoring polynomials, rational expressions, exponents, radicals, graphing, and system of equations. Additional topics include graphs and their translations and reflections, functions, exponential and logarithmic functions, graphs of quadratic and polynomial functions, nonlinear systems of equations, polynomial and rational inequalities, and an introduction to conic sections.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 recognize and solve various types of equations, inequalities, and systems of equations, and related applications.
 factor a variety of polynomials.
 collect like terms in simplifying polynomial, rational, exponential, and logarithmic expressions.
 sketch graphs of lines and conics and functions.
 associate equations and information from tables or charts with their corresponding graphs.
 recognize and explain the concept of a mathematical function/relation and use functional notation appropriately to formulate solutions.
 compare and contrast the properties of a mathematical function and its inverse function.
 analyze and solve applications related to linear, rational, and radical equations.
 define what a logarithm is and solve logarithmic equations and applications.
 define what an exponential function is and solve exponential equations and applications.
MATH 131 Combined Algebra  Part I
 Units:3
 Hours:54 hours LEC
 Prerequisite:Through the Los Rios Placement Process or successful completion of Prealgebra.
 Advisory:CISC 100, CISC 300, or CISC 305 with a grade of "C" or better.
 Catalog Date:August 1, 2024
This course is the first of three parts covering combined algebra in a masterybased learning environment. It emphasizes problemsolving skills. Topics include linear equations and inequalities, integer exponents, polynomials, systems of linear equations, the rectangular coordinate system, graphs and equations of lines, and related applications. Students who complete this course during the first half of the semester may sign up immediately for MATH 132. For the most updated information, please visit the Math Learning Center (MLC) web page on the ARC website. Completion of MATH 131 AND MATH 132 with grades of "C" or better meets the prerequisite for MATH 133, MATH 110, MATH 120, and MATH 125.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 solve linear equations and inequalities.
 graph linear equations and inequalities.
 apply appropriate solving techniques to solve systems of linear equations.
 demonstrate addition, subtraction, and multiplication of polynomials.
 apply properties of exponents.
 set up and solve application problems using appropriate algebraic methods.
MATH 132 Combined Algebra  Part II
 Units:3
 Hours:54 hours LEC
 Prerequisite:Through the Los Rios Placement Process.
 Catalog Date:August 1, 2024
This course is the second of three parts covering combined algebra in a masterybased learning environment. It emphasizes problemsolving skills throughout the course. Topics include polynomial factorization, rational expressions and equations, radical expressions and equations, rational exponents, and related applications. Students who complete this course during the first half of the semester may sign up immediately for MATH 133. For the most updated information, please visit the MMLC web page on the ARC website. Completion of MATH 131 AND MATH 132 with grades of "C" or better meets the prerequisite for MATH 133, MATH 110, MATH 120, and MATH 125.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 apply appropriate factoring techniques to polynomials.
 demonstrate factoring and algebraic techniques to solve quadratic equations.
 simplify rational expressions and solve equations with rational expressions.
 identify and solve variation applications.
 use roots, radicals, and exponents in simplifying expressions.
 solve equations with radical expressions.
 set up and solve application problems using appropriate algebraic methods.
MATH 133 Combined Algebra  Part III
 Units:3
 Hours:54 hours LEC
 Prerequisite:Through the Los Rios Placement Process.
 General Education:AA/AS Area II(b)
 Catalog Date:August 1, 2024
This course is the third of three parts covering combined algebra in a masterybased learning environment. It emphasizes problemsolving skills. Topics include function evaluation and notation, inverse functions, solving quadratic equations, complex numbers, graphs of quadratic functions, exponential and logarithmic functions, properties of logarithms, conic sections, and related applications. For the most updated information, please visit the Math Learning Center (MLC) web page on the ARC website. Completion of MATH 131, MATH 132, AND MATH 133 with grades of "C" or better is equivalent to the completion of MATH 120 or MATH 125 or MATH 129.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 differentiate between a mathematical function and relation.
 evaluate functions using function notation.
 solve quadratic equations using a variety of algebraic methods.
 analyze and graph quadratic functions.
 analyze and graph exponential and logarithmic functions.
 solve exponential and logarithmic equations using algebraic properties.
 classify and construct graphs of conic sections.
 set up and solve application problems using appropriate algebraic methods.
MATH 145 Mathematics for the Trades
 Units:1.5
 Hours:23 hours LEC; 12 hours LAB
 Prerequisite:None.
 Catalog Date:August 1, 2024
This course introduces mathematics applicable to technical programs of study. Topics include the use of mathematical operators on whole numbers, fractions, and decimals. Additional content includes fundamentals of algebra, basic geometry, and triangle trigonometry. This course is intended for those in PreApprenticeship programs or other technical educational programs. Completion of this course does not fulfill any prerequisites for any course, including MATH courses, at American River College.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 solve application problems which require basic algebraic skills.
 evaluate problems using addition, subtraction, multiplication, and division of whole numbers.
 evaluate problems using addition, subtraction, multiplication, and division of fractions.
 evaluate problems using addition, subtraction, multiplication, and division of decimals.
 apply basic geometric formulas and properties to solve problems.
 apply and use trigonometric ratios of right triangles to solve application problems.
 apply dimensional analysis in performing technical calculations.
 use units and dimensions in measurement problems involving customary units and metric terms.
 demonstrate problemsolving techniques of applications using ratio and proportions.
MATH 294 Topics in Mathematics
 Units:0.5  4
 Hours:9  72 hours LEC
 Prerequisite:None.
 Catalog Date:August 1, 2024
This course is designed to give students an opportunity to study topics in mathematics not included in current course offerings. Individualized topics are developed to foster, complement and build upon arithmetic, geometric and algebraic skills with an emphasis on critical thinking.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 define the vocabulary of a given mathematical topic.
 translate openended problems into the given mathematical topic.
 apply techniques (processes or algorithms) to manipulate, illustrate or compute the mathematical objects of the given mathematical topic.
 generalize the techniques (processes or algorithms) of the given mathematical topic to other settings.
MATH 295 Independent Studies in Mathematics
 Units:1  3
 Hours:54  162 hours LAB
 Prerequisite:None.
 Catalog Date:August 1, 2024
Independent Study is an opportunity for the student to extend classroom experience in this subject, while working independently of a formal classroom situation. Independent study is an extension of work offered in a specific class in the college catalog. To be eligible for independent study, students must have completed the basic regular catalog course at American River College. They must also discuss the study with a professor in this subject and secure approval. Only one independent study for each catalog course will be allowed.
MATH 299 Experimental Offering in Mathematics
 Units:0.5  4
 Prerequisite:None.
 Catalog Date:August 1, 2024
This is the experimental courses description.
MATH 300 Introduction to Mathematical Ideas
 Units:3
 Hours:54 hours LEC
 Prerequisite:MATH 120, 125, 129, or 133 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:August 1, 2024
This course makes fundamental concepts and processes more meaningful for nonmathematics majors through a study of several mathematical topics, including the history of mathematics, numeration systems, logic, geometry, algebraic modeling, combinatorics, probability, statistics, sets, matrices, consumer mathematics, equations and inequalities, functions and graphs, problem solving, graph theory, voting and apportionment, and number theory. It is not recommended for students entering elementary school teaching or business administration majors.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 discuss several branches of mathematics, including their history and uses beyond mathematics.
 identify appropriate procedures and solve exercises from selected mathematical topics.
 apply critical thinking skills to solve exercises in new settings.
 explain the process and results of several mathematical procedures.
MATH 310 Mathematical Discovery
 Units:3
 Hours:54 hours LEC
 Prerequisite:MATH 110 with a grade of "C" or better or successful completion of high school geometry, AND MATH 120, 125, 129, or 133 with a "C" or better, or placement through the assessment process. Geometry is the only high school course that can be used to meet the prerequisite.
 Transferable:CSU; UC
 General Education:AA/AS Area II(b); CSU Area B4
 Catalog Date:August 1, 2024
This course explores mathematical patterns and relations as well as the formulation and proof of conjectures. Topics from number theory, probability and statistics, and geometry are investigated. This course is recommended for students interested in a degree in education.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 explore and discover mathematical patterns and relations for a variety of problems from number theory, statistics, and geometry.
 formulate conjectures based on exploration in a variety of problems from number theory, geometry, and statistics.
 prove or find a counterexample for proposed conjectures.
 analyze statistical data.
 calculate probabilities by applying appropriate statistical concepts.
MATH 311 Mathematical Concepts for Elementary School Teachers  Number Systems
 Units:3
 Hours:54 hours LEC
 Prerequisite:MATH 120, 125, 129, or 133 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
 CID:CID MATH 120
 Catalog Date:August 1, 2024
This course focuses on the development of quantitative reasoning skills through indepth, integrated explorations of topics in mathematics, including history of real number systems and subsystems, basic number theory, sets and relations, logic, mathematical induction, and current national and state curriculum standards for mathematics. It emphasizes comprehension and critical analysis of mathematical concepts and applications of logical reasoning.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 summarize the historical development of numeration systems, including an examination of the base ten numeration system and an analysis of place value systems in general using exponent and place value notation
 perform calculations with place value systems
 evaluate the equivalence of numeric algorithms and explain the advantages and disadvantages of equivalent algorithms in different circumstances
 apply algorithms from number theory to determine divisibility in a variety of settings
 analyze least common multiples and greatest common divisors and their role in standard algorithms
 explain the concept of rational numbers, using both ratio and decimal representations; analyze the arithmetic algorithms for these two representations; and justify their equivalence
 analyze the structure and properties of whole, rational, and real number systems; define the concept of rational and irrational numbers, including their decimal representation; and illustrate the use of a number line representation
 develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communication, connections, modeling, reasoning, and representation
 apply basic tools such as sets, functions, and logic together with deductive or inductive reasoning to solve problems from an elementary to advanced level of math
 develop activities implementing curriculum standards
MATH 320 Symbolic Logic
 Same As:PHIL 324
 Units:3
 Hours:54 hours LEC
 Prerequisite:MATH 120, 125, 129, or 133 with a grade of "C" or better, or placement through the assessment process.
 Transferable:CSU; UC
 General Education:AA/AS Area II(b)
 CID:CID PHIL 210
 Catalog Date:August 1, 2024
This course is an introduction to symbolic logic. It includes a study of the logic of sentences (propositional logic) and the logic of classes and relations (predicate logic), together with an introduction to the nature of deductive systems. This course is not open to students who have completed PHIL 324.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 represent statements of English in wellformed sentences of predicate logic.
 prove the validity of statements and arguments in predicate logic using formal proof techniques.
 apply truth table or truth tree methods to determine semantic properties such as invalidity and consistency.
 construct interpretations that satisfy statements and sets of statements.
 distinguish classical first order logical systems from other logical systems.
MATH 333 Introduction to College Algebra
 Units:3
 Hours:54 hours LEC
 Prerequisite:Through the Los Rios Placement Process or High School Algebra 2 or Integrated Math 3 or Intermediate Algebra.
 Transferable:CSU; UC
 General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
 Catalog Date:August 1, 2024
This course is a transferlevel algebra course for majors in the Liberal Arts. This course also offers instruction in algebra that is necessary for precalculuslevel Business, Science, Technology, Engineering and Math (BSTEM) coursework. Topics include absolute value, polynomial, rational, radical, exponential, and logarithmic functions; solving equations involving these functions; graphing these functions using transformations; solving linear and nonlinear inequalities; systems of equations; complex numbers; and inverse functions.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 analyze and investigate properties of functions.
 synthesize results from the graphs and/or equations of functions.
 solve and apply equations including linear, absolute value, polynomial, radical, rational, exponential, and logarithmic equations.
 solve linear and nonlinear systems of equations and inequalities.
 apply functions and other algebraic techniques to model real world applications.
 recognize the relationship between functions and their inverses graphically and algebraically.
 apply transformations to the graphs of functions.
MATH 340 Calculus for Business and Economics
 Units:3
 Hours:54 hours LEC
 Prerequisite:MATH 120, 129, or 133 with a grade of "C" or better, or placement through the assessment process.
 Transferable:CSU; UC (UC credit limitation: MATH 340, 350 & 400 combined: maximum credit, one course)
 General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
 CID:CID MATH 140
 Catalog Date:August 1, 2024
This course introduces how differential calculus and integral calculus are used in the fields of business, economics, social science, and biological science. Topics include finding limits, applying various rules to find derivatives of polynomial, rational, exponential, and logarithmic functions, as well as using derivatives to analyze marginal cost, revenue, and profit. It is not recommended for mathematics and physical science majors.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 evaluate and explore functions that represent quantities important in business, including profit, average cost, supply, and demand.
 compute limits graphically, numerically, and analytically.
 find derivatives of various functions, including polynomial, rational, exponential, and logarithmic functions using the Power, Product, Quotient, and Chain Rules.
 find the equation of the tangent line to a polynomial, rational, exponential, or logarithmic function, using derivatives.
 sketch the graph of functions using horizontal and vertical asymptotes, intercepts, first and second derivatives to determine intervals of increase and decrease, maximum and minimum values, intervals of concavity, and points of inflection.
 recognize and solve business applications that call for derivatives of single or multivariable functions including implicit differentiation, related rates, and optimization problems.
 find antiderivatives of various functions using substitution, integration by parts, and other methods.
 evaluate definite integrals using the Fundamental Theorem of Calculus.
 recognize and solve business applications that call for antiderivatives of single variable or multivariable functions.
MATH 342 Modern Business Mathematics
 Units:3
 Hours:54 hours LEC
 Prerequisite:MATH 120, 129, or 133 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:August 1, 2024
This course is designed around applications of mathematics in economic and business contexts. Specific topics include functions and related business formulas, tables and graphs, finance (interest and exponential models in economics), rates of change, applications and optimization, and linear programming.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 analyze formulas, tables, graphs, and data sets in order to form conclusions or make predictions.
 identify and graph linear, quadratic, rational, polynomial, exponential, and logarithmic functions.
 formulate and apply exponential growth or decay functions pertaining to business applications.
 calculate both present and future values involving simple interest, compound interest, and annuities.
 analyze applications of annuities involving loan amortization and sinking funds, applying necessary formulas.
 evaluate rates of change for a variety of elementary functions and apply them to marginal analysis.
 find and interpret optimum values related to business applications.
 solve linear programming problems by the graphical approach.
MATH 355 Calculus for Biology and Medicine I
 Units:4
 Hours:72 hours LEC
 Prerequisite:MATH 373 or 375 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:August 1, 2024
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.
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
 General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
 Catalog Date:August 1, 2024
This course covers matrix algebra with eigenvalues and eigenvectors, systems of linear equations, functions of several variables, partial derivatives, systems of differential equations, and applications to biology and medicine.
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 372 College Algebra for Calculus
 Units:4
 Hours:72 hours LEC
 Prerequisite:MATH 120, 129, or 133 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:August 1, 2024
This course provides a rigorous treatment of collegelevel algebra and its applications, with a particular focus on preparing students for the calculus sequence for Science, Technology, Engineering, and Mathematics (STEM) majors. Topics include polynomial, rational, radical, exponential, absolute value, and logarithmic functions, graphs, and equations; systems of equations; the theory of polynomial equations; analytic geometry including conics; and an introduction to sequences and series. Emphasis is given to analytical reasoning and problemsolving.
This course may be taken concurrently with MATH 373, Trigonometry for Calculus. Completion of both MATH 372 AND MATH 373 with grades of "C" or better meets the prerequisite for MATH 400, Calculus I.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 analyze and investigate properties of functions.
 synthesize connections between equations of functions and their graphs, including asymptotic behavior, intercepts, and vertices.
 apply transformations to the graphs of functions, including quadratic, absolute value, radical, rational, logarithmic, and exponential functions.
 recognize the relationship between a function and its inverse both graphically and algebraically.
 solve equations and applications involving rational, linear, polynomial, radical, absolute value, exponential, and logarithmic equations.
 solve systems of equations and inequalities.
 apply techniques for determining zeros of polynomials and roots of equations.
 apply functions and other algebraic techniques to model real world STEM applications.
 analyze conics algebraically and graphically.
 use formulas to find the sum of both finite and infinite series.
MATH 373 Trigonometry for Calculus
 Units:4
 Hours:72 hours LEC
 Prerequisite:MATH 120, 129, or 133 with a grade of "C" or better, or placement through the assessment process.
 Advisory:MATH 110; or completion of high school geometry
 Transferable:CSU; UC
 General Education:AA/AS Area II(b); CSU Area B4
 Catalog Date:August 1, 2024
This course provides a rigorous treatment of trigonometry and its applications, with a particular focus on preparing students for the calculus sequence for science, technology, engineering, and mathematics (STEM) majors. It emphasizes the study of trigonometric functions from numerical, graphical, and algebraic descriptions. Topics include functions and their graphs, transformations of functions, geometric properties of circles and triangles, degree and radian measurements of angles, right triangle trigonometry, reference angle trigonometry, unit circle trigonometry, graphs and transformations of trigonometric functions, verifying and applying trigonometric identities, inverse trigonometric functions, solving trigonometric equations, solving triangles using the Law of Sines and the Law of Cosines, vectors, the polar coordinate system, and roots and powers of complex numbers including De Moivre's Theorem. This course may be taken concurrently with MATH 372, College Algebra for Calculus. Completion of both MATH 372 AND MATH 373 with grades of "C" or better meets the prerequisite for MATH 400, Calculus I.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 convert between degree measure and radian measure of angles.
 graph angles in the coordinate plane and identify the reference angle.
 define the six trigonometric functions in terms of right triangles, the rectangular coordinate system, and the unit circle.
 apply the right triangle definitions of the six trigonometric functions to solve right triangles.
 evaluate trigonometric functions of angles in both degrees and radians.
 evaluate trigonometric functions of special angles in both degrees and radians without a calculator.
 recognize and create the graphs of the basic trigonometric functions.
 graph transformations of the basic trigonometric functions by thinking about amplitude, period, phase shift, and vertical shift.
 simplify expressions using trigonometric identities.
 find function values by making use of identities.
 prove a variety of identities.
 evaluate and graph inverse trigonometric functions.
 evaluate compositions of trigonometric and inverse trigonometric functions.
 solve a variety of trigonometric equations.
 use the Laws of Sines and Cosines to solve oblique triangles.
 solve application problems that involve right and oblique triangles.
 represent a vector both graphically and in ai+bj form.
 perform basic vector operations: addition, subtraction, and scalar multiplication, as well as represent these operations graphically and algebraically.
 calculate powers and roots of complex numbers using De Moivre's Theorem.
 convert between polar and rectangular coordinates and equations.
 graph polar equations.
MATH 375 PreCalculus
 Units:6
 Hours:108 hours LEC
 Prerequisite:MATH 120, 129, or 133 with a grade of "C" or better, or placement through the assessment process.
 Advisory:MATH 110; or completion of high school geometry
 Transferable:CSU; UC
 General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
 Catalog Date:August 1, 2024
This course provides a rigorous treatment of the foundational mathematical concepts and skills that will prepare students for the calculus sequence for science, technology, engineering, and mathematics (STEM) majors. Topics include polynomial, absolute value, rational, radical, exponential, and logarithmic functions, with graphing and applications; trigonometric functions and their inverses, including graphs, proving identities, trigonometric equations, and solving triangles; systems of equations and inequalities; analytic geometry and conics; vectors and polar coordinates; and an introduction to sequences and series. It emphasizes analytical reasoning and problemsolving.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 graph functions and relations and investigate their properties.
 synthesize connections between equations of functions and their graphs, including asymptotic behavior, intercepts, and vertices.
 apply transformations to the graphs of functions and relations, including quadratic, absolute value, radical, rational, logarithmic, and exponential functions.
 recognize the relationship between a function and its inverse both graphically and algebraically.
 solve equations and applications involving linear, absolute value, polynomial, rational, radical, exponential, and logarithmic equations.
 apply techniques for determining zeros of polynomials and roots of equations.
 apply functions to model real world applications.
 identify special triangles and their related angle and side measures.
 evaluate the trigonometric function at an angle whose measure is given in degrees and radians.
 graph the basic trigonometric functions and apply changes in period, amplitude, vertical shift, and horizontal shift to generate new graphs.
 evaluate and graph inverse trigonometric functions.
 solve trigonometric equations, triangles, and applications.
 manipulate and simplify trigonometric expressions and prove trigonometric identities.
 convert between polar and rectangular coordinates and graph polar equations.
 calculate powers and roots of complex numbers using DeMoivre's Theorem.
 represent a vector (a quantity with magnitude and direction) in the form <a, b> and ai+bj.
 solve systems of equations and inequalities.
 analyze conics algebraically and graphically.
 use formulas to find the sum of both finite and infinite series.
 use the Binomial Theorem to expand (a+b)^n.
MATH 400 Calculus I
 Units:5
 Hours:90 hours LEC
 Prerequisite:MATH 370 (PreCalculus Mathematics), OR MATH 375 (PreCalculus Mathematics), OR MATH 372 (College Algebra for Calculus) AND MATH 373 (Trigonometry for Calculus) with grades of "C" or better, or placement through the assessment process.
 Transferable:CSU; UC (UC credit limitation:MATH 340, 350 & 400 combined: maximum credit, one course)
 General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
 CID:CID MATH 210; Part of CID MATH 900S
 Catalog Date:August 1, 2024
This course is an introduction to differential and integral calculus. It covers limits, continuity, differentiation and integration of algebraic, trigonometric, logarithmic, exponential, and other transcendental functions. Some applications are also covered.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 evaluate limits graphically, analytically, and by using L'Hopital's Rule.
 compute derivatives using the definition of derivative.
 apply differentiation rules to various types of functions.
 recognize and solve application problems that require use of derivatives.
 apply antidifferentiation rules to various types of functions.
 compute definite integrals using the Fundamental Theorem of Calculus.
 recognize and solve application problems that require use of antiderivatives.
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 351 & 401 combined: maximum credit, one course)
 General Education:CSU Area B4; IGETC Area 2
 CID:CID MATH 220; Part of CID MATH 900S
 Catalog Date:August 1, 2024
This course is a continuation of MATH 400. It builds on the methods of integration learned in MATH 400, and also covers improper integrals, sequences, infinite series, power series, polar coordinates, and parametric and polar equations. Many calculus applications are also included.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 identify and use properties of logarithmic, exponential, and inverse trigonometric functions to evaluate integrals.
 evaluate integrals using the techniques of integration by parts, trig substitution, partial fractions, and rationalizing substitutions.
 recognize and evaluate limits in indeterminate forms and improper integrals.
 determine the convergence or divergence of sequences and series, find power series representations for certain transcendental functions, and apply appropriate Calculus techniques to evaluate derivatives and integrals of power series.
 rewrite, analyze and graph equations in three forms: rectangular, parametric, and polar; using appropriate calculus techniques.
 use various integration techniques to solve applications, including area, volume, and arc length.
 solve separable differential equations to determine growth and decay functions.
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:CSU Area B4; IGETC Area 2
 CID:CID MATH 230
 Catalog Date:August 1, 2024
This course is a continuation of MATH 401. It extends the concepts of limits, derivatives, and integrals to vectorvalued functions and multivariate functions. The topics include multivariate functions, partial derivatives, extrema of multivariate functions, iterated integrals, development of vector calculus, line integrals, threedimensional analytic geometry, and Green's, Gauss' (Divergence), and Stokes' Theorems. Many applications of calculus are also covered.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 analyze and graph two and threedimensional functions, vectors, vectorvalued functions, and geometric surfaces and solids in order to solve for various geometric quantities and to represent motion in space.
 perform vector operations: addition, subtraction, scalar multiplication, dot products, and cross products.
 determine the equations of lines and planes in space, including tangent planes to a surface.
 find the limit of a multivariate function at a point and determine the differentiability of a multivariate function.
 evaluate partial derivatives and apply them to find local extrema and test for saddle points of multivariate functions.
 apply Lagrange multipliers to solve optimization problems with constraints.
 compute the arc length of a curve.
 set up and evaluate iterated integrals in rectangular, cylindrical, and spherical coordinates to calculate the area, volume, mass, and center of mass for a surface or solid.
 find the gradient of a scalar field and the divergence and curl of a vector field.
 set up and evaluate line and surface integrals using Green's, Gauss', and Stokes' Theorems and use results to solve application problems involving vector fields.
MATH 410 Introduction to Linear Algebra
 Units:3
 Hours:54 hours LEC
 Prerequisite:MATH 401 with a grade of "C" or better
 Advisory:MATH 402
 Transferable:CSU; UC
 General Education:CSU Area B4; IGETC Area 2
 CID:CID MATH 250; Part of CID MATH 910S
 Catalog Date:August 1, 2024
This course provides an introduction to linear algebra including matrices, determinants, vector spaces, inner product spaces, linear transformations, and eigenvectors. It is intended for majors in mathematics, engineering, economics, science, and related fields. This course emphasizes cogent reasoning, mathematical proof, and problem solving.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 solve systems of linear equations by reducing an augmented matrix to rowechelon or reduced rowechelon form.
 determine whether a linear system is consistent or inconsistent; for consistent systems, characterize solutions as unique or infinitely many and write parametric solutions for systems with infinitely many solutions.
 evaluate matrix expressions using properties of matrix algebra.
 compute the transpose, determinant, adjoint, and inverse of matrices if defined for a given matrix.
 determine if a subset of a vector space is a vector space, and if so, prove that the subset is a subspace.
 determine if a given set of vectors is linearly independent, and if so, prove that this determination is correct.
 determine if a given set of vectors is a basis for a vector space, and if so, prove that this determination is correct and find the basis and dimension of spaces such as those associated with matrices and linear transformations or the intersection of two subspaces.
 calculate inner products, use properties of inner products to determine angle and orthogonality, and use an orthonormal basis to to find the projection of a vector on a space.
 determine if a function that maps two vectors from a vector space to a scalar is an inner product on that vector space.
 construct orthogonal and orthonormal bases using the GramSchmidt Process for a given basis.
 construct the orthogonal diagonalization of a symmetric matrix.
 determine the matrix for a linear transformation on Euclidean 2space or 3space, and for a given linear transformation, determine kernel, range, rank, nullity, and whether the linear transformation is an isomorphism.
 compute the characteristic polynomial, eigenvalues, eigenvectors, and eigenspaces for both matrices and linear transformations.
 use eigenvalues and eigenvectors in applications and diagonalization.
 prove basic results in linear algebra using accepted proofwriting techniques including linear independence of vectors, properties of subspaces, linearity, injectivity, surjectivity, properties of eigenvectors, and properties of eigenvalues.
MATH 420 Differential Equations
 Units:4
 Hours:72 hours LEC
 Prerequisite:MATH 401 with a grade of "C" or better
 Advisory:MATH 402
 Transferable:CSU; UC
 General Education:CSU Area B4; IGETC Area 2
 CID:CID MATH 240; Part of CID MATH 910S
 Catalog Date:August 1, 2024
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:
 formulate and analyze mathematical models using ordinary differential equations.
 categorize a given differential equation by type, order, and linearity.
 determine existence and uniqueness of solutions of an initial value problem for the firstorder ordinary differential equation.
 solve elementary firstorder and secondorder ordinary differential equations (linear and nonlinear) using analytical methods.
 solve ordinary differential equations using power series.
 solve higher order ordinary differential equations with constant coefficients using analytical techniques.
 solve systems of linear ordinary differential equations with constant coefficients using analytical methods.
 assess situations in which a differential equation can be solved more efficiently with the Laplace Transform or the Inverse Laplace Transform and apply the transform to the equation when appropriate.
MATH 480 Honors Seminar in Mathematics
 Units:1
 Hours:18 hours LEC
 Prerequisite:None.
 Transferable:CSU
 Catalog Date:August 1, 2024
Honors Seminar in Mathematics is a oneunit intensive course. The course is taught in a seminar format where work is done independently in pursuit of solutions to challenging problems in mathematics in consultation with the instructor. Seminar participants will explore strategies and techniques for solving problems and present their solutions to the class.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 perform critical analysis and exploration when confronted with a nonstandard challenging mathematics problem by constructing models and developing cogent strategies to find a solution.
 demonstrate mastery and understanding of various mathematical topics from precalculus.
 present work in a seminar to a critical audience.
 explore and attack mathematics problems with depth and significance.
MATH 495 Independent Studies in Mathematics
 Units:1  3
 Hours:54  162 hours LAB
 Prerequisite:None.
 Transferable:CSU
 Catalog Date:August 1, 2024
Independent Study is an opportunity for the student to extend classroom experience in this subject, while working independently of a formal classroom situation. Independent study is an extension of work offered in a specific class in the college catalog. To be eligible for independent study, students must have completed the basic regular catalog course at American River College. They must also discuss the study with a professor in this subject and secure approval. Only one independent study for each catalog course will be allowed.
MATH 499 Experimental Offering in Mathematics
 Units:0.5  4
 Prerequisite:None.
 Transferable:CSU
 Catalog Date:August 1, 2024
This is the experimental courses description.
Mathematics Support (MATHS) Courses
MATHS 33 Support for Introduction to College Algebra
 Units:2
 Hours:36 hours LEC
 Prerequisite:None.
 Corequisite:MATH 333
 Catalog Date:August 1, 2024
This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 333 (Introduction to College Algebra). Students taking this course must be concurrently enrolled in the corresponding section of MATH 333. The content of this course is designed to provide arithmetic and algebraic support to students as they learn related concepts in their corequisite course. Topics and homework assignments are often connected to assignments in the corequisite course. This course is graded Pass/No Pass.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 analyze and investigate properties of functions.
 choose and apply appropriate techniques to factor a variety of polynomials.
 synthesize results from the graphs and/or equations of functions.
 solve and apply equations including linear, absolute value, polynomial, radical, rational, exponential, and logarithmic equations.
 solve linear and nonlinear systems of equations and inequalities.
 apply functions and other algebraic techniques to model realworld applications.
 recognize the relationship between functions and their inverses graphically and algebraically.
 apply transformations to the graphs of functions.
MATHS 45 Support for Business Mathematics
 Units:2
 Hours:36 hours LEC
 Prerequisite:None.
 Corequisite:MATH 340 or 342
 Catalog Date:August 1, 2024
This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Calculus for Business and Economics (MATH 340) and Modern Business Mathematics (MATH 342). Students taking this course must be concurrently enrolled in the corresponding section of MATH 340 or MATH 342. The content of this course is designed to provide arithmetic and algebraic support to students as they learn related concepts in their corequisite course. Topics and homework assignments are often connected to students’ assignments in the corequisite course. This course is graded Pass/No Pass.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 apply learning strategies to achieve success in Calculus for Business and Economics or Modern Business Mathematics.
 use real numbers to perform arithmetic operations in the evaluation of algebraic functions.
 simplify expressions and solve equations involving polynomial, rational, radical, exponential, and logarithmic functions.
 analyze the structure of multivariable equations utilizing graphs, tables, and algebraic methods.
 utilize algebraic techniques and problem solving strategies to solve application problems.
MATHS 60 Support for Calculus I
 Units:2
 Hours:36 hours LEC
 Prerequisite:None.
 Corequisite:MATH 400
 Catalog Date:August 1, 2024
This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Calculus I. Students taking this course must be concurrently enrolled in the corresponding section of MATH 400. The content of this course is designed to provide arithmetic, algebra, geometry, trigonometry, and learning skills support to students as they learn concepts in their Calculus I course. Topics and homework assignments are often connected to assignments in the Calculus I course. This course is graded Pass/No Pass.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 use learning strategies to achieve success in Calculus I.
 recall the methods from arithmetic necessary to be successful in Calculus I.
 apply the methods from algebra necessary to be successful in Calculus I.
 apply the methods from geometry necessary to be successful in Calculus I.
 apply the methods from trigonometry necessary to be successful in Calculus I.
MATHS 72 Support for College Algebra for Calculus
 Units:2
 Hours:36 hours LEC
 Prerequisite:None.
 Corequisite:MATH 372
 Catalog Date:August 1, 2024
This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 372 (College Algebra for Calculus). Students taking this course must be concurrently enrolled in the corresponding section of MATH 372. The content of this course is designed to provide arithmetic and algebraic support to students as they learn related concepts in their corequisite course. Topics and homework assignments are often connected to assignments in the corequisite course. This course is graded Pass/No Pass.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 use mathematics support skills to solve equations and inequalities and manipulate expressions.
 use mathematics support skills to solve systems of equations and inequalities.
 use mathematics support skills to demonstrate a deep understanding of functions and their properties.
 apply learning strategies to achieve success in College Algebra for Calculus.
MATHS 73 Support Course for Trigonometry for Calculus
 Units:2
 Hours:36 hours LEC
 Prerequisite:None.
 Corequisite:MATH 373
 Catalog Date:August 1, 2024
This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Trigonometry for Calculus (MATH 373). Students taking this course must be concurrently enrolled in the corresponding section MATH 373. The course content is designed to provide arithmetic, algebra, geometry and learning skills support to students as they learn related concepts in their corequisite course. Topics and homework assignments are often connected to students’ assignments in the corequisite course. This course is graded Pass/No Pass.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 recall the methods from arithmetic necessary to be successful in Trigonometry for Calculus
 review the methods from algebra necessary to be successful in Trigonometry for Calculus
 demonstrate an understanding of the methods from geometry necessary to be successful in Trigonometry for Calculus
 apply learning strategies to achieve success in Trigonometry for Calculus
MATHS 75 Support for PreCalculus
 Units:3
 Hours:54 hours LEC
 Prerequisite:None.
 Corequisite:MATH 375
 Catalog Date:August 1, 2024
This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 375 (PreCalculus). Students taking this course must be concurrently enrolled in the corresponding section of MATH 375. The content of this course is designed to provide arithmetic, algebra, geometry, and learning skills support to students as they learn related concepts in their corequisite course. Topics and homework assignments are often connected to assignments in the corequisite course. This course is graded Pass/No Pass.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 apply learning strategies to achieve success in PreCalculus.
 recall the methods from arithmetic necessary to be successful in PreCalculus.
 review the methods from algebra necessary to be successful in PreCalculus.
 demonstrate an understanding of the methods from geometry necessary to be successful in PreCalculus.
MATHS 95 Support for Introduction to Mathematical Ideas
 Units:2
 Hours:36 hours LEC
 Prerequisite:None.
 Corequisite:MATH 300
 Catalog Date:August 1, 2024
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). Students taking this course must be concurrently enrolled in the corresponding section of MATH 300. The content of this course is designed to provide arithmetic and algebraic support to students as they learn related concepts in their corequisite course. Topics and homework assignments are often connected to assignments in the corequisite course. This course is graded Pass/No Pass.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 apply learning strategies to achieve success in Introduction to Mathematical Ideas (MATH 300).
 use support mathematics skills to identify appropriate procedures and solve exercises from selected mathematical topics.
 use support mathematics skills to apply critical thinking skills to solve exercises in new settings.
 use support mathematics skills to explain the process and results of several mathematical procedures.
MATHS 299 Experimental Offering in Mathematics Support
 Units:0.5  4
 Prerequisite:None.
 Catalog Date:August 1, 2024
This is the experimental courses description.
MATHS 499 Experimental Offering in Mathematics Support
 Units:0.5  4
 Prerequisite:None.
 Catalog Date:August 1, 2024
This is the experimental courses description.
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:August 1, 2024
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). Students taking this course must be concurrently enrolled in the corresponding section of STAT 300. The content of this course is designed to help students develop effective learning strategies, and to provide arithmetic, algebraic, and geometric support as they learn concepts in the statistics course. Topics and homework assignments are often connected to assignments in the statistics course. Support using the required statistical technology package is also included. This course is graded Pass/No Pass.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 apply learning strategies to achieve success in statistics.
 use problem solving techniques in the context of data analysis and statistical methods.
 demonstrate relevant arithmetic, algebraic, and geometric skills in the context of statistics.
 apply mathematical and statistical skills in realworld settings and interpret the results in context.
STAT 105 Statway, Part I
 Units:6
 Hours:108 hours LEC
 Prerequisite:MATH 32 or 42 with a grade of "C" or better, or placement through the assessment process.
 Advisory:Eligible for ENGRD 310 or ENGRD 312 AND ENGWR 300; OR ESLR 340 AND ESLW 340.
 Transferable:CSU
 Catalog Date:August 1, 2024
This is the first semester of a twosemester course that introduces the concepts of probability and statistics with requisite arithmetic and algebraic topics integrated throughout. It is structured to serve students planning to transfer and continue studies in humanities or social sciences. Statistics topics emphasize data analysis and include methods for collecting data, graphical and numerical descriptive statistics, correlation, linear regression, simple exponential regression, and introduction to probability. Algebra topics include proportional relationships (including variation) with applications, expressions, linear equations and systems with applications, functions, quadratic and exponential equations, and linear and exponential models. Learning strategies for success with an emphasis on study skills, resource acquisition, and maintaining a positive perspective towards learning are also discussed and applied.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 identify methods of obtaining data and related advantages and disadvantages of each.
 organize and display data using appropriate tables and graphs.
 summarize a given data set using appropriate numerical summaries.
 analyze data by computing measures of central tendency, measures of dispersion, and measures of position.
 make meaningful and appropriate comparisons of distributions of data collected from two or more different groups.
 analyze bivariate data for linear trends using the leastsquares regression model and the correlation coefficient.
 develop and apply the concept of numeracy to investigate and describe quantitative relationships and solve problems in a variety of contexts.
 solve problems that require the use of ratios, rates, proportions, and scaling.
 express realworld and quantitative situations with equations, inequalities, expressions, tables, verbal descriptions, symbols, and graphs.
 solve application problems involving equations, systems of equations, and inequalities and explain how results relate to the original context.
 apply functions as a way of modeling a correspondence between two variables in linear, quadratic, exponential, and logarithmic situations.
 solve problems involving exponential growth and decay in formulas, graphs, tables, and applications.
 calculate and interpret probabilities.
 estimate probabilities (including conditional probabilities) empirically and using simulation.
 use statistical software or graphing calculator to calculate single variable and analyze the results.
 apply learning strategies to achieve success in mathematics.
STAT 300 Introduction to Probability and Statistics
 Units:4
 Hours:72 hours LEC
 Prerequisite:Through the Los Rios Placement Process or successful completion of Algebra II/Integrated Math 3 or Intermediate Algebra.
 Transferable:CSU; UC (UC credit limitation: STAT 300, 305, and PSYC 330 combined: maximum credit, one course )
 General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
 CID:CID MATH 110
 Catalog Date:August 1, 2024
This course is an introduction to probability and statistics. Topics include elementary principles and applications of descriptive statistics, counting principles, elementary probability principles, probability distributions, estimation of parameters, hypothesis testing, linear regression and correlation, and Analysis of Variance (ANOVA). Applications use data from various disciplines including business, social sciences, psychology, life and health sciences, and education. Statistical analysis using a computer statistics package or graphing calculator is required.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 identify methods of obtaining data and related advantages and disadvantages of each.
 distinguish between types of data as well as their different scales of measurement and corresponding implications.
 organize and display data appropriately using tables and graphs.
 analyze data by computing measures of central tendency, measures of dispersion, and measures of position.
 analyze bivariate data for linear trends using the leastsquares regression model and the correlation coefficient.
 distinguish between probability models appropriate to different chance events and calculate probability according to these methods.
 analyze both discrete and continuous probability distributions, including binomial probability, normal distributions, and tdistributions by examining and interpreting areas under the graph of a histogram or a normal curve.
 apply inferential statistical methods to compare population parameters, make predictions, and draw conclusions about hypotheses.
 select the appropriate hypothesis test, perform the necessary computations and comparisons for the test (including significance of pvalues and type I/II errors), and explain the conclusion of the test.
 test the significance of correlation and make predictions based on linear trends using the leastsquares regression model.
 create and interpret confidence interval estimates for population parameters based on appropriate probability models.
 analyze and interpret applications using data from various disciplines including business, social sciences, psychology, life sciences, health science, and education.
 use statistical software or graphing calculator to calculate singlevariable and twovariable statistics and analyze the results.
STAT 305 Statway, Part II
 Units:6
 Hours:108 hours LEC
 Prerequisite:STAT 105 with a grade of "C" or better
 Transferable:CSU; UC (UC credit limitation: STAT 300, 305, and PSYC 330 combined: maximum credit, one course; Maximum credit limitation: 4 semester/6 quarter units. STAT 105 and 305 must both be completed w/ "C" or better. )
 General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
 Catalog Date:August 1, 2024
This is the second semester of a twosemester course that introduces the concepts of probability and statistics with requisite arithmetic and algebraic topics integrated throughout. It is structured to serve students planning to transfer and continue studies in humanities or social sciences. Statistics topics emphasize data analysis and include basic concepts of probability; confidence intervals; hypothesis tests for means, proportions, and variance; chisquared tests; and ANOVA (Analysis of Variance). Algebra topics include proportional relationships (including variation) with applications, expressions, linear equations and systems with applications, functions, quadratic and exponential equations, and linear and exponential/logarithmic models. Learning strategies for success with an emphasis on study skills, resource acquisition, and maintaining a positive perspective towards learning are also discussed and applied. Both parts of Statway must be completed with a grade of "C" or better to receive credit for transferlevel statistics.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 identify methods of obtaining data and related advantages and disadvantages of each.
 distinguish between types of data as well as their different scales of measurement and corresponding implications.
 organize and display data appropriately using tables and graphs.
 analyze data by computing measures of central tendency, measures of dispersion, and measures of position.
 analyze bivariate data for linear trends using the leastsquares regression model and the correlation coefficient.
 analyze both discrete and continuous probability distributions, including binomial probability and normal distribution, by examining and interpreting areas under the graph of a histogram or a normal curve.
 apply inferential statistical methods to compare population parameters, make predictions, and draw conclusions about hypothesis.
 apply the concept of numeracy to investigate and describe quantitative relationships and solve problems in a variety of contexts.
 select the appropriate hypothesis test, perform the necessary computations and comparisons for the test (including significance of pvalues and type I/II errors), and explain the conclusion of the test.
 test the significance of correlation and make prediction based on linear trends using the leastsquares regression model.
 create and interpret confidence interval estimates for population parameters based on appropriate probability models.
 analyze and interpret applications using data from various disciplines including business, social sciences, psychology, life sciences, health science, and education.
 use statistical software or graphing calculator to calculate single variable and twovariable statistics and analyze the results.
 make conjectures about the behavior of a function in a given context.
 apply learning strategies to achieve success in mathematics.
STAT 480 Introduction to Probability and Statistics  Honors
 Units:4
 Hours:72 hours LEC
 Prerequisite:MATH 120, 125, 129, or 133 with a grade of "C" or better, or placement through the assessment process.
 Advisory:Placement into ENGWR 300.
 Transferable:CSU; UC
 General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
 CID:CID MATH 110
 Catalog Date:August 1, 2024
This course is an introduction to probability and statistics designed for students in the honors program. Topics include elementary principles and applications of descriptive statistics, counting principles, elementary probability principles, probability distributions, estimation of parameters, hypothesis testing, linear regression and correlation, and Analysis of Variance (ANOVA). Applications use data from various disciplines including business, social sciences, psychology, life and health sciences, and education. Statistical analysis using a computer statistics package is required. This honors section uses an intensive instructional methodology designed to challenge motivated students, and includes a capstone project. This course is not open to students who have completed STAT 300.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
 identify methods of obtaining data and related advantages and disadvantages of each.
 distinguish between types of data as well as their different scales of measurement and corresponding implications.
 organize and display data appropriately using tables and graphs.
 analyze data by computing measures of central tendency, measures of dispersion, and measures of position.
 analyze bivariate data for linear trends using the leastsquares regression model and the correlation coefficient.
 distinguish between probability models appropriate to different chance events and calculate probability according to these methods.
 analyze both discrete and continuous probability distributions, including binomial probability, normal distributions, and tdistributions by examining and interpreting areas under the graph of a histogram or a normal curve.
 apply inferential statistical methods to compare population parameters, make predictions, and draw conclusions about hypotheses.
 select the appropriate hypothesis test, perform the necessary computations and comparisons for the test (including significance of pvalues and type I/II errors), and explain the conclusion of the test.
 test the significance of correlation and make predictions based on linear trends using the leastsquares regression model.
 create and interpret confidence interval estimates for population parameters based on appropriate probability models.
 analyze and interpret applications using data from various disciplines including business, social sciences, psychology, life sciences, health science, and education.
 use statistical software or graphing calculator to calculate singlevariable and twovariable statistics and analyze the results.
STAT 495 Independent Studies in Statistics
 Units:1  3
 Hours:54  162 hours LAB
 Prerequisite:None.
 Transferable:CSU
 Catalog Date:August 1, 2024
Independent Study is an opportunity for the student to extend classroom experience in this subject, while working independently of a formal classroom situation. Independent study is an extension of work offered in a specific class in the college catalog. To be eligible for independent study, students must have completed the basic regular catalog course at American River College. They must also discuss the study with a professor in this subject and secure approval. Only one independent study for each catalog course will be allowed.
STAT 499 Experimental Offering in Statistics
 Units:0.5  4
 Prerequisite:None.
 Transferable:CSU
 Catalog Date:August 1, 2024
This is the experimental courses description.
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