Lower-Division Math Courses

MATH 004. Introduction to College Mathematics for Business and the Social Sciences (5)

Lecture, 5 hours.

Prerequisite(s): a sufficiently high score on the Mathematics Advisory Examination, as determined by the Mathematics Department. Not open to students in the Bourns College of Engineering or the College of Natural and Agricultural Sciences or to students majoring in Economics or Business Economics.

Covers functions and their graphs, including linear and polynomial functions, zeroes, and inverse functions as well as exponential, logarithmic, and trigonometric functions and their inverses. Also includes counting, including elementary probability. Involves applications to business and social sciences. Credit is awarded for only one of MATH 004, MATH 005, or MATH 008A.

MATH 005. Precalculus (5)

Lecture, 5 hours.

Prerequisite(s): a sufficiently high score on the Mathematics Advisory Examination, as determined by the Mathematics Department.

A study of inequalities, absolute value, functions, graphing, logarithms, trigonometry, roots of polynomials, counting, vectors, and other elementary concepts of mathematics Credit is awarded for only one of MATH 004, MATH 005, or MATH 008A.

MATH 005P. MATH 005 Support Practicum (1)

Practicum, 2-4 hours; individual study, 2-4 hours.

Prerequisite(s): Students must be enrolled in UCR’s Summer Bridge MATH 005 program.

Covers understanding course content and developing thinking and problem-solving skills. Introduces university life through exposure to test-taking techniques, effective note-taking strategies, time management, and university procedures and practices. Offered in summer only. Graded Satisfactory (S) or No Credit (NC).

MATH 008A. Introduction to College Mathematics for the Sciences (5)

Lecture, 5 hours.

Prerequisite(s): a sufficiently high score on the Mathematics Advisory Examination, as determined by the Mathematics Department.

Covers functions and their graphs, including linear and polynomial functions, zeroes, and inverse functions as well as exponential, logarithmic and trigonometric functions and their inverses. Also includes counting, including elementary probability. Involves applications to the natural sciences and engineering. Credit is awarded for only one of MATH 004, MATH 005, or MATH 008A.

MATH 008B. Introduction to College Mathematics for the Sciences (5)

Lecture, 5 hours.

Prerequisite(s): MATH 008A with a grade of “C-” or better or a sufficiently high score on the Mathematics Advisory Examination, as determined by the Mathematics Department. Not intended for students who have been awarded a grade of “C-” or better in MATH 005.

Involves further study of trigonometry and analytic geometry. Introduction to the differential calculus of functions of a single variable. Credit is awarded for only one of MATH 008B, MATH 009A, or MATH 09HA.

MATH 009A. First-Year Calculus (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): MATH 005 with a grade of “C-” or better or equivalent.

Introduction to the differential calculus of functions of one variable. Credit is awarded for only one of MATH 008B, MATH 009A, or MATH 09HA.

MATH 009B. First-Year Calculus (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): MATH 008B with a grade of “C-” or better or MATH 009A with a grade of “C-” or better or MATH 09HA with a grade of “C-” or better.

Introduction to the integral calculus of functions of one variable. Credit is awarded for only one of MATH 009B or MATH 09HB.

MATH 009C. First-Year Calculus (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): MATH 009B with a grade of “C-” or better or MATH 09HB with a grade of “C-” or better.

Further topics from integral calculus, improper integrals, infinite series, Taylor’s series, and Taylor’s theorem. Credit is awarded for only one of MATH 009C or MATH 09HC.

MATH 09HA. First-Year Honors Calculus (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): a sufficiently high score on the placement examination, as determined by the Mathematics Department.

Honors course corresponding to MATH 009A for students with strong mathematical backgrounds. Emphasis is on theory and rigor. Credit is awarded for only one of MATH 008B, MATH 009A, or MATH 09HA.

MATH 09HB. First-Year Honors Calculus (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): a score of 4 or higher on the AB Advanced Placement Test in Mathematics or MATH 009A with a grade of “A-” or better or MATH 09HA with a grade of “A-” or better.

Honors course corresponding to MATH 009B for students with strong mathematical backgrounds. Emphasis is on theory and rigor. Credit is awarded for only one of MATH 009B or MATH 09HB.

MATH 09HC. First-Year Honors Calculus (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): MATH 009B with a grade of “A-” or better or MATH 09HB with a grade of “A-” or better.

Honors course corresponding to MATH 009C for students with strong mathematical backgrounds. Emphasis is on theory and rigor. Credit is awarded for only one of MATH 009C or MATH 09HC.

MATH 010A. Calculus of Several Variables (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): MATH 009B with a grade of “C-” or better or MATH 09HB with a “C-” or better or equivalent.

Topics include Euclidean geometry, matrices and linear functions, determinants, partial derivatives, directional derivatives, Jacobians, gradients, chain rule, and Taylor’s theorem for several variables.

MATH 010B. Calculus of Several Variables (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): MATH 010A with a grade of "C-" or better or equivalent.

Covers vectors; differential calculus, including implicit differentiation and extreme values; multiple integration; line integrals; vector field theory; and theorems of Gauss, Green, and Stokes.

MATH 046. Introduction to Ordinary Differential Equations (4)

Lecture, 3 hours; discussion, 1 hour.

Prerequisite(s): MATH 009B with a grade of "C-" or better or MATH 09HB with a grade of "C-" or better or equivalent.

Introduction to first-order equations, linear second-order equations, and Laplace transforms, with applications to the physical and biological sciences. Only one of the following sequences, PHYS 002A, PHYS 002B, PHYS 002C, or PHYS 040A, PHYS 040B, PHYS 040C may be taken for credit.