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:January 1, 2022
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.
MATH 25 Computational Arithmetic
- Units:3
- Hours:54 hours LEC
- Prerequisite:None.
- Advisory:Placement through the math assessment process.
- Catalog Date:January 1, 2022
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.
MATH 32 Pre-Algebra
- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 25 or 41 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:January 1, 2022
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.
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:January 1, 2022
This course is the first of two parts covering algebra readiness in a mastery-based 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.
MATH 42 Algebra Readiness - Part II
- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 41 with a grade of "C" or better
- Catalog Date:January 1, 2022
This course is the second of two parts covering algebra readiness in a mastery-based learning environment. It introduces the fundamentals of pre-algebra, 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.
MATH 100 Elementary Algebra
- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 32 or 42 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:January 1, 2022
This course covers the fundamental concepts and operations of algebra and incorporates problem-solving 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.
MATH 110 Elementary Geometry
- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 100 or 132 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:January 1, 2022
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 problem-solving strategies, elementary logic, and writing proofs.
MATH 120 Intermediate Algebra
- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 100 or 132 with a grade of "C" or better, or placement through the assessment process.
- General Education:AA/AS Area II(b)
- Catalog Date:January 1, 2022
This course extends and reviews the concepts of elementary algebra while incorporating applications and problem-solving 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.
MATH 125 Intermediate Algebra for Statistics and Liberal Arts
- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 100 or 132 with a grade of "C" or better, or placement through the assessment process.
- General Education:AA/AS Area II(b)
- Catalog Date:January 1, 2022
This is an intermediate algebra course for non-STEM 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 real-world data. This course does not meet the prerequisite for STEM-track math courses.
MATH 129 Elementary and Intermediate Algebra
- Units:9
- Hours:162 hours LEC
- Prerequisite:MATH 32 or 42 with a grade of "C" or better, or placement through the assessment process.
- General Education:AA/AS Area II(b)
- Catalog Date:January 1, 2022
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.
MATH 131 Combined Algebra - Part I
- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 32 or 42 with a grade of "C" or better, or placement through the assessment process.
- 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.
- Catalog Date:January 1, 2022
This course is the first of three parts covering combined algebra in a mastery-based learning environment. It emphasizes problem-solving 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.
MATH 132 Combined Algebra - Part II
- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 131 with a grade of "C" or better
- Catalog Date:January 1, 2022
This course is the second of three parts covering combined algebra in a mastery-based learning environment. It emphasizes problem-solving 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.
MATH 133 Combined Algebra - Part III
- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 132 with a grade of "C" or better
- General Education:AA/AS Area II(b)
- Catalog Date:January 1, 2022
This course is the third of three parts covering combined algebra in a mastery-based learning environment. It emphasizes problem-solving 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.
MATH 145 Mathematics for the Trades
- Units:1.5
- Hours:23 hours LEC; 12 hours LAB
- Prerequisite:None.
- Catalog Date:January 1, 2022
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 Pre-Apprenticeship 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.
MATH 294 Topics in Mathematics
- Units:0.5 - 4
- Hours:9 - 72 hours LEC
- Prerequisite:None.
- Catalog Date:January 1, 2022
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.
MATH 295 Independent Studies in Mathematics
- Units:1 - 3
- Hours:54 - 162 hours LAB
- Prerequisite:None.
- Catalog Date:January 1, 2022
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:January 1, 2022
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:January 1, 2022
This course makes fundamental concepts and processes more meaningful for non-mathematics 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.
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:January 1, 2022
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.
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
- C-ID:C-ID MATH 120
- Catalog Date:January 1, 2022
This course focuses on the development of quantitative reasoning skills through in-depth, 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.
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)
- C-ID:C-ID PHIL 210
- Catalog Date:January 1, 2022
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.
MATH 325 Problem-Solving
- 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
- General Education:AA/AS Area II(b); CSU Area B4
- Catalog Date:January 1, 2022
This course focuses on the development of specific strategies and skills necessary to solve real-world and advanced mathematics problems. It emphasizes the development of logical, organizational, and divergent thinking, as well as written and oral communication skills, individual and group work, and clear presentation of mathematical work. Topics include drawing a diagram, eliminating possibilities, making a systematic list, looking for a pattern, guessing and checking, solving an easier related problem, working backwards, using algebraic representation, and applying the method of finite differences.
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
- C-ID:C-ID MATH 140
- Catalog Date:January 1, 2022
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.
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:January 1, 2022
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.
MATH 355 Calculus for Biology and Medicine I
- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 373 with a grade of "C" or better, or placement through the assessment process.
- Advisory:MATH 370
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- Catalog Date:January 1, 2022
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.
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:January 1, 2022
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. This course is a superset of MATH 351, treating additional topics and covering them in more depth.
MATH 370 Pre-Calculus Mathematics
- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 373 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
- C-ID:C-ID MATH 155
- Catalog Date:January 1, 2022
This course provides foundational mathematics and problems that require critical thinking in preparation for the calculus sequence for science, technology, engineering, and mathematics (STEM) majors. Topics include rigorous treatment of polynomial, rational, logarithmic, exponential, and trigonometric functions, including graphing and applications, as well as systems of linear and non-linear equations and inequalities. This course also covers analytic geometry, conic sections, vectors, parametric equations, and polar equations.
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:January 1, 2022
This course provides a rigorous treatment of college-level 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 problem-solving.
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.
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
- General Education:AA/AS Area II(b); CSU Area B4
- Catalog Date:January 1, 2022
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.
MATH 375 Pre-Calculus
- 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:January 1, 2022
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 problem-solving.
MATH 400 Calculus I
- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 370 (Pre-Calculus 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
- C-ID:C-ID MATH 210; Part of C-ID MATH 900S
- Catalog Date:January 1, 2022
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.
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
- C-ID:C-ID MATH 220; Part of C-ID MATH 900S
- Catalog Date:January 1, 2022
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.
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
- C-ID:C-ID MATH 230
- Catalog Date:January 1, 2022
This course is a continuation of MATH 401. It extends the concepts of limits, derivatives, and integrals to vector-valued functions and multivariate functions. The topics include multivariate functions, partial derivatives, extrema of multivariate functions, iterated integrals, development of vector calculus, line integrals, three-dimensional analytic geometry, and Green's, Gauss' (Divergence), and Stokes' Theorems. Many applications of calculus are also covered.
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
- C-ID:C-ID MATH 250; Part of C-ID MATH 910S
- Catalog Date:January 1, 2022
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.
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
- C-ID:C-ID MATH 240; Part of C-ID MATH 910S
- Catalog Date:January 1, 2022
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.
MATH 480 Honors Seminar in Mathematics
- Units:1
- Hours:18 hours LEC
- Prerequisite:MATH 370 with a grade of "C" or better
- Transferable:CSU; UC
- Catalog Date:January 1, 2022
Honors Seminar in Mathematics is a one-unit 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.
MATH 495 Independent Studies in Mathematics
- Units:1 - 3
- Hours:54 - 162 hours LAB
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:January 1, 2022
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:January 1, 2022
This is the experimental courses description.