# Lower-Division

## MATH 2 College Algebra for Calculus

Operations on real numbers, complex numbers, polynomials, and rational expressions; exponents and radicals; solving linear and quadratic equations and inequalities; functions, algebra of functions, graphs; conic sections; mathematical models; sequences and series.

### Credits

5

#### Requirements

Prerequisite(s): mathematics placement (MP) score of 100 or higher. Students may not enroll in or receive credit for MATH 2 after receiving credit with a 'C' or better in AM 3, MATH 3, AM 11A, MATH 11A, MATH 19A, MATH 20A or equivalents.

Fall, Summer

## MATH 2S College Algebra for Calculus

This two-credit, stretch course offers students two quarters to master material covered in MATH 2: operations on real numbers, complex numbers, polynomials, and rational expressions; exponents and radicals; solving linear and quadratic equations and inequalities; functions, algebra of functions, graphs; conic sections; mathematical models; sequences and series. After successful completion of this course in the first quarter, students enroll in MATH 2 the following quarter to complete the sequence and earn an additional 5 credits.

### Credits

2

The Staff

#### Requirements

Prerequisite(s): mathematics placement (MP) score of 100 or higher.

## MATH 2T Preparatory Math: Tutorial

Independent study of algebra and modern mathematics using adaptive learning software. Instruction emphasizes clear mathematical communication and reasoning when working with sets, equations, functions, and graphs. Drop in labs, online forums, and readings provide opportunities for further learning and exploration.

### Credits

2

Debra Lewis

#### Requirements

Prerequisite(s): mathematics placement (MP) score of 100 or higher.

Yes

## MATH 3 Precalculus

Inverse functions and graphs; exponential and logarithmic functions, their graphs, and use in mathematical models of the real world; rates of change; trigonometry, trigonometric functions, and their graphs; and geometric series. Students cannot receive credit for both MATH 3 and AM 3.

### Credits

5

#### Requirements

Prerequisite(s): MATH 2 or mathematics placement (MP) score of 200 or higher. Students may not enroll in or receive credit for MATH 3 after receiving credit with a 'C' or better in AM 11A, MATH 11A, MATH 19A, MATH 20A or equivalents.

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 4 Mathematics of Choice and Argument

Techniques of analyzing and creating quantitative arguments. Application of probability theory to questions in justice, medicine, and economics. Analysis and avoidance of statistical bias. Understanding the application and limitations of quantitative techniques.

### Credits

5

#### Requirements

Prerequisite(s): MATH 2, or mathematics placement (MP) score of 200 or higher, or AP Calculus AB examination score of 3 or higher.

SR

## MATH 11A Calculus with Applications

A modern course stressing conceptual understanding, relevance, and problem solving. The derivative of polynomial, exponential, and trigonometric functions of a single variable is developed and applied to a wide range of problems involving graphing, approximation, and optimization. Students cannot receive credit for both this course and MATH 19A, or AM 11A, or AM 15A, or ECON 11A.

### Credits

5

#### Requirements

Prerequisite(s): MATH 3 or AM 3; or mathematics placement (MP) score of 300 or higher; or AP Calculus AB exam score of 3 or higher.

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 11B Calculus with Applications

Starting with the fundamental theorem of calculus and related techniques, the integral of functions of a single variable is developed and applied to problems in geometry, probability, physics, and differential equations. Polynomial approximations, Taylor series, and their applications conclude the course. Students cannot receive credit for this course and MATH 19B, or AM 11B, or AM 15B, or ECON 11B.

### Credits

5

#### Requirements

Prerequisite(s): MATH 11A or MATH 19A or AM 15A or AP Calculus AB exam score of 4 or 5, or BC exam score of 3 or higher, or IB Mathematics Higher Level exam score of 5 or higher.

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 19A Calculus for Science, Engineering, and Mathematics

The limit of a function, calculating limits, continuity, tangents, velocities, and other instantaneous rates of change. Derivatives, the chain rule, implicit differentiation, higher derivatives. Exponential functions, inverse functions, and their derivatives. The mean value theorem, monotonic functions, concavity, and points of inflection. Applied maximum and minimum problems. Students cannot receive credit for both this course and MATH 11A, or AM 11A, or AM 15A, or ECON 11A.

### Credits

5

#### Requirements

Prerequisite(s): MATH 3; or mathematics placement (MP) score of 400 or higher; or AP Calculus AB exam score of 3 or higher.

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 19B Calculus for Science, Engineering, and Mathematics

The definite integral and the fundamental theorem of calculus. Areas, volumes. Integration by parts, trigonometric substitution, and partial fractions methods. Improper integrals. Sequences, series, absolute convergence and convergence tests. Power series, Taylor and Maclaurin series. Students cannot receive credit for both this course and MATH 11B, or AM 11B, or AM 15B, or ECON 11B.

### Credits

5

#### Requirements

Prerequisite(s): MATH 19A or MATH 20A or AP Calculus AB exam score of 4 or 5, or BC exam score of 3 or higher, or IB Mathematics Higher Level exam score of 5 of higher.

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 20A Honors Calculus

Methods of proof, number systems, binomial and geometric sums. Sequences, limits, continuity, and the definite integral. The derivatives of the elementary functions, the fundamental theorem of calculus, and the main theorems of differential calculus.

### Credits

5

#### Requirements

Prerequisite(s): mathematics placement (MP) score of 500 higher; or AP Calculus AB examination score of 4 or 5; or BC examination of 3 or higher; or IB Mathematics Higher Level examination score of 5 or higher.

MF

## MATH 20B Honors Calculus

Orbital mechanics, techniques of integration, and separable differential equations. Taylor expansions and error estimates, the Gaussian integral, Gamma function and Stirling's formula. Series and power series, numerous applications to physics.

### Credits

5

#### Requirements

Prerequisite(s): MATH 20A.

MF

## MATH 21 Linear Algebra

Systems of linear equations matrices, determinants. Introduces abstract vector spaces, linear transformation, inner products, the geometry of Euclidean space, and eigenvalues. Students cannot receive credit for this course and AM 10.

### Credits

5

#### Requirements

Prerequisite(s): MATH 11A or MATH 19A or MATH 20A or AM 11A or AM 15A.

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 22 Introduction to Calculus of Several Variables

Functions of several variables. Continuity and partial derivatives. The chain rule, gradient and directional derivative. Maxima and minima, including Lagrange multipliers. The double and triple integral and change of variables. Surface area and volumes. Applications from biology, chemistry, earth sciences, engineering, and physics. Students cannot receive credit for this course and MATH 23A.

### Credits

5

#### Requirements

Prerequisite(s): MATH 11B or MATH 19B or MATH 20B or AM 15B or AP calculus BC exam score of 4 or 5.

MF

Winter, Summer

## MATH 23A Vector Calculus

Vectors in n-dimensional Euclidean space. The inner and cross products. The derivative of functions from n-dimensional to m-dimensional Euclidean space is studied as a linear transformation having matrix representation. Paths in 3-dimensions, arc length, vector differential calculus, Taylor's theorem in several variables, extrema of real-valued functions, constrained extrema and Lagrange multipliers, the implicit function theorem, some applications. Students cannot receive credit for this course and MATH 22 or AM 30.

### Credits

5

#### Requirements

Prerequisite(s): MATH 19B or MATH 20B or AP calculus BC exam score of 4 or 5.

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 23B Vector Calculus

Double integral, changing the order of integration. Triple integrals, maps of the plane, change of variables theorem, improper double integrals. Path integrals, line integrals, parametrized surfaces, area of a surface, surface integrals. Green's theorem, Stokes' theorem, conservative fields, Gauss' theorem. Applications to physics and differential equations, differential forms.

### Credits

5

#### Requirements

Prerequisite(s): MATH 23A.

MF

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 24 Ordinary Differential Equations

First and second order ordinary differential equations, with emphasis on the linear case. Methods of integrating factors, undetermined coefficients, variation of parameters, power series, numerical computation. Students cannot receive credit for this course and AM 20.

### Credits

5

#### Requirements

Prerequisite(s): MATH 22 or MATH 23A; MATH 21 is recommended as preparation.

#### Quarter offered

Fall, Winter, Spring, Summer

## MATH 99 Tutorial

### Credits

5

#### Quarter offered

Fall, Winter, Spring

## MATH 99F Tutorial

### Credits

2

Yes

#### Quarter offered

Fall, Winter, Spring