# Lower-Division

## MATH 10A Basic Calculus

Algebra and trigonometry review, differentiation, applications of differentiation, integration, applications of integration, series, vectors and matrices, differential equations. Designed for students who desire to learn calculus with less detail than in the corresponding 11A-B sequence. Students cannot receive credit for both a 10 course and the corresponding 11 course.

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## MATH 10B Basic Calculus

Algebra and trigonometry review, differentiation, applications of differentiation, integration, applications of integration, series, vectors and matrices, differential equations. Designed for students who desire to learn calculus with less detail than in the corresponding 11A-B sequence. Students cannot receive credit for both a 10 course and the corresponding 11 course

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## MATH 12C Applied Linear Algebra

Systems of linear equations, matrices, determinants, euclidean spaces, eigenvalues, and eigenvectors. Extensive computational work on computers in a campus Macintosh lab. Integrates both the computational and the theoretical aspects of linear algebra. No prior computer experience is needed. Concurrent enrollment in course 12L is required. One quarter of college mathematics is recommended.

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## MATH 13 Vector Calculus

The derivative as a linear transformation. Directional derivatives, gradients, divergence, and curl. Maxima and minima. Integrals on paths and surfaces. Green, Stokes, and Gauss theorems.

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Fall

## MATH 28 Introduction to Computational Number Theory

Prime numbers, congruences, Euclid's algorithm. The theorems of Fermat and Lagrange. The reduction of arithmetic calculations to the case of prime-power modulus. The use of quadratic residues. Computational aspects of primality testing, and factorization techniques. Students cannot receive credit for this course and course 18. High school algebra is recommended; knowledge of a computer language is useful.

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## MATH 28L Laboratory for Computational Number Theory

Laboratory sequence illustrating topics covered in course 28. One three-hour session per week in microcomputer laboratory. Concurrent enrollment in course 28 is required.

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## MATH 50 Introduction to Fractal Geometry I: Iterated Function Systems and L-Systems

Definition and measurement of fractal dimension, self-similarity and self-affinity, iterated function and L-systems, random fractals, diffusion limited aggregation models, multi-fractals, Julia and Mandelbrot sets, rewriting systems, image compression, chaos and fractals. Concurrent enrollment in course 50L is required.

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## MATH 50L Fractal Geometry I Laboratory

Laboratory sequence illustrating topics covered in course 150. One three-hour session per week in microcomputer laboratory. Concurrent enrollment in course 150 is required.

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## MATH 80A What is Mathematics?

A broad overview of the subject, intended primarily for liberal arts students. What do mathematicians do, and why do they do it? Examines the art of proving theorems, from both the philosophical and aesthetic points of view, using examples such as non-Euclidean geometrics, prime numbers, abstract groups, and uncountable sets. Emphasis on appreciating the beauty and variety of mathematical ideas. Includes a survey of important results and unsolved problems which motivate mathematical research.

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## MATH 80B Nature of Mathematics

A survey course, aimed at non-science students, providing an understanding of some fundamental concepts of higher mathematics. Is mathematics a natural science? Do mathematicians discover or invent? Discussion of such questions in connection with such topics as numbers (whole, prime, negative, irrational, round, imaginary, binary, transfinite, infinitesimal, etc.), logic, symmetry, various types of geometry, and some recent developments. Basic high school algebra and geometry is sufficient background. Students cannot receive credit for this course and course 80A.

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