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| The Mathematics Department offers about 170 sections of undergraduate courses each year. Of these, about 70 are large lecture courses, primarily in calculus, with enrollments ranging from 90 to 350 students, and an average enrollment of about 150 students. The remaining courses form a broad spectrum serving the various mathematics majors and also students in engineering, the physical sciences, the biological sciences, the social sciences, and teacher training. About 90 courses (30 each Quarter) are Upper Division courses, which have an average enrollment of about 25 students and which are capped at about 40. About five or so of these each Quarter have fewer than 15 students, and they provide a good environment for the student to learn and to develop closer ties with faculty members. | ||||||||||||||||||
| In addition to its own course offerings, the Mathematics Department administers the Program in Computing, which offers about ten sections of courses in computer programming and computer science each quarter. The Mathematics Department also collaborates with the Statistics Department in administering its offering of statistics courses. This comprises about five sections of upper division statistics courses each quarter, together with several sections of the lower division course, Statistics 50. | ||||||||||||||||||
There are three calculus sequences serving different clientele. The first is a three-quarter calculus sequence, Math 3ABC, that is aimed at the biological sciences. It covers the essentials of one-variable and multivariable calculus, and it includes a module on calculus-based probability. The second calculus sequence is the six-quarter sequence Math 31AB, Math 32AB, Math 33AB. It is the standard calculus sequence for engineering and physical science students. Single-variable calculus is treated in Math 31AB and multivariable calculus in Math 32AB, culminating in the theorems of Green, Gauss, and Stokes. The course Math 33A covers linear algebra and ordinary differential equations, and the course Math 33B covers infinite series, including Fourier series. Different combinations of these courses are required for various majors by other departments. For instance, the mathematics courses required for the Bachelor of Science in General Chemistry are Math 31AB, Math 32A, and Math 33A. (Math 33A does not have Math 32B as a prerequisite, only Math 32A; and Math 32A has only Math 31B as a prerequisite.) The third calculus sequence is Math 31A followed by Math 31E, which is tailored to the needs of the students in economics. This brief course sequence moves more rapidly into multivariable calculus and optimization techniques, at the expense of some of the more technical single-variable calculus material required by physical scientists and engineers. Associated with the multivariable calculus courses 32A and 32B respectively are two one-unit computer laboratory courses Math 32AL and Math 32BL. |
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| Before beginning calculus, students should have a thorough precalculus preparation. The precalculus course Math 1 is designed to provide students with this preparation. In order to enroll in Math 31A, students must take and pass the Mathematics Diagnostic Test at the specified level required for admission to the course, or they must take and pass Math 1 with a grade of C- or better. | ||||||||||||||||||
| In addition to calculus and precalculus, there are several specialized lower division courses. The largest is the course Math 2, which is aimed at students in the social sciences with a modest background in mathematics. It has no prerequisites, and it satisfies the quantitative reasoning requirement of the College of Letters and Science. One lecture section of Math 2 is offered each quarter, and the average enrollment is between 250 and 300 students. | ||||||||||||||||||
| Several courses are designed for prospective elementary and secondary math teachers. The one-year sequence Math 38ABC serves to train teachers of elementary and middle school mathematics. Enrollment in this course sequence is carefully controlled. Another course sequence for the professional training of prospective middle school and high school teachers is Math 370AB. | ||||||||||||||||||
| The Department offers one upper division course of general interest, the course Math 106 in the history of mathematics. A minimal background in calculus is required for the history course. | ||||||||||||||||||
| For mathematics students, the main bridge between lower division and upper division mathematics is the course in linear algebra, Math 115A. It is required of all the various math majors. Occasionally a sequel, Math 115B, is offered. | ||||||||||||||||||
| Math M112: Introduction to Set Theory Math 114AB: Logic and Computability |
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| Math 61: Introduction to Discrete Structures Math 113: Combinatorics |
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| Math 110ABC: Algebra Math 111: Theory of Numbers Math 117: Algebra for Applications |
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| Math 120AB: Differential Geometry Math 121: Introduction to Topology Math 123: Foundations of Geometry |
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| Math 131AB: Analysis Math 131C: Topics in Analysis Math 132: Complex Analysis for Applications Math 135AB: Ordinary Differential Equations Math 136: Partial Differential Equations |
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| Math 142: Mathematical Modeling Math 143: Analytic Mechanics Math 146: Methods of Applied Mathematics |
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| Math 149: Mathematics of Computer Graphics Math 151AB: Applied Numerical Methods (formerly Math 141AB) Math 153: Numerical Methods for Partial Differential Equations (formerly Math 148A) Math 157: Software Techniques for Scientific Computation |
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| Math 164: Linear Programming (formerly Math 144) Math 167: Game Theory (formerly Math 147) |
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| Math M170A: Probability Theory (formerly Math M150A) Math 170B: Probability Theory (formerly Math 150B) Math 171: Stochastic Processes (formerly Math 151) |
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| Math 172AB: Actuarial Mathematics | ||||||||||||||||||
| Math 181: Mathematics of Finance | ||||||||||||||||||
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The Mathematics Department offers several honors course sequences. Students with a record of A's and B's in their math courses are encouraged to take honors courses. The Mathematics Department is experimenting with its Lower Division honors offerings. Fall Quarter 1997 it is offering honors course sequences beginning with both 31BH and with 31CH. The Upper Division honors course sequences fit into the following scheme. |
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The Mathematics Department also offers Math 191H, Mathematics Honors Seminar, usually once a year in the Fall Quarter. See the Honors Program for information. |
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| Math 195 provides an opportunity for students interested in teaching to work in local schools and study issues in mathematics education. | ||||||||||||||||||
| Several students each year receive either two or four units credit for individual or group studies or research under the course title Math 197, Individual Studies in Mathematics, or Math 199, Directed Research or Senior Project in Mathematics. | ||||||||||||||||||
The Mathematics Department, like many other departments at UCLA, has undergone a downsizing during the 1990's. As a result of the restructuring, a considerable number of changes have been made since the 1995-97 UCLA General Catalog went to print. More than 25 quarter courses that appear in the 1995-97 UCLA General Catalog have been deleted, and five others (Math 111ABC, 133, 134) have been amalgamated to form two courses (Math 111, Math 131C). The computer track of the calculus sequence, Math 31AQ, Math 31BQ, Math 32AQ, Math 32BQ, has been replaced by a sequence of one-unit computer-calculus laboratory courses 32AL-32BL. Additionally, several of the courses have been renumbered. At the same time the Mathematics Department continues to design and implement new course offerings reflecting current interests and research developments. A new course in scientific computing, Math 157, was introduced in the academic year 1996-97 and will continue to be offered once a year. A new course in the mathematics of finance, Math 181, had its initial offering Fall Quarter 1997. A one-unit computer laboratory course Math 33AL is being designed by Ronald Miech to accompany Math 33A, and an applied linear algebra course is being developed by Ming Gu as an alternative for Math 115A. |
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