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2020-21 UCSC General Catalog
2019-20 UCSC General Catalog

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.

5

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

Fall, Summer

This two-credit, stretch course offers students two quarters to master material covered in course 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 course 2 the following quarter to complete the sequence and earn an additional 5 credits.

2

The Staff

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

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.

2

Debra Lewis

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

Yes

Fall

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. AM 3 can substitute for MATH 3.

5

Prerequisite(s): MATH 2 or mathematics placement (MP) score of 200 or higher.

MF

Fall, Winter, Spring, Summer

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.

5

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

SR

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.

5

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

Fall, Winter, Spring, Summer

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.

5

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

Fall, Winter, Spring, Summer

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.

5

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

MF

Fall, Winter, Spring, Summer

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.

5

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

Fall, Winter, Spring, Summer

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.

5

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

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.

5

Prerequisite(s): MATH 20A.

MF

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.

5

MF

Fall, Winter, Spring, Summer

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 course 23A.

5

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

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 course 22. (Formerly Multivariable Calculus.)

5

MF

Fall, Winter, Spring, Summer

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. (Formerly Multivariable Calculus.)

5

Prerequisite(s): MATH 23A.

MF

Fall, Winter, Spring, Summer

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.

5

Fall, Winter

5

Fall, Winter, Spring

2

Yes

Fall, Winter, Spring