| source UC Santa Cruz (X) |
level |
department Mathematics (X) |
Enrollment restricted to graduate students. Enrollment restricted to graduate students.
Score: 7.1519613 Details | Listing | Web page
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. Prerequisite(s): placement exam score of 12 or higher.
Score: 7.1519613 Details | Listing | Web page
Inverse functions and graphs; exponential and logorithmic 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 course 3 and Applied Mathematics and Statistics 3. Applied Mathematics and Statistics 3 can substitute for course 3. Prerequisite(s): course 2 or placement exam score of 20 or higher. (General Education Code(s): Q.)
Score: 7.1519613 Details | Listing | Web page
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. Prerequisite(s): course 2, or placement exam score of 12 or higher, or AP Calculus AB exam score of 3 or higher. Enrollment limited to 54. (General Education Code(s): Q.)
Score: 7.1519613 Details | Listing | Web page
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 course 19A or Applied Mathematics and Statistics 11A or Economics 11A. Prerequisite(s): course 3 or Applied Mathematics and Statistics 3; or placement exam score of 31 or higher; or AP Calculus AB exam score of 3 or higher. (General Education Code(s): IN, Q.)
Score: 7.1519613 Details | Listing | Web page
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 course 19B, or Applied Mathematics and Statistics 11B, or Economics 11B. Prerequisite(s): course 11A 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. (General Education Code(s): IN, Q.)
Score: 7.1519613 Details | Listing | Web page
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 course 11A or Applied Mathematics and Statistics 11A or Economics 11A. Prerequisite(s): course 3 or Applied Mathematics and Statistics 3 or placement exam score of 40 or higher or AP Calculus AB exam score of 3 or higher. (General Education Code(s): IN, Q.)
Score: 7.1519613 Details | Listing | Web page
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 course 11B, Applied Math and Statistics 11B, or Economics 11B. Prerequisite(s): course 19A 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. (General Education Code(s): IN, Q.)
Score: 7.1519613 Details | Listing | Web page
Challenging course designed to approach single-variable calculus from the perspective of modern mathematics. Emphasis is on the evolution and historical development of core concepts underlying calculus and analysis. Prerequisite(s): placement exam score of 46 or higher; or AP Calculus AB exam score of 4 or 5; or BC exam of 3 or higher; or IB Mathematics Higher Level exam score of 5 or higher. Enrollment limited to 60. (General Education Code(s): IN, Q.)
Score: 7.1519613 Details | Listing | Web page
Challenging course designed to approach single-variable calculus from the perspective of modern mathematics. Emphasis is on the evolution and historical development of core concepts underlying calculus and analysis. Prerequisite(s): course 20A. Enrollment limited to 60. (General Education Code(s): IN, Q.)
Score: 7.1519613 Details | Listing | Web page
Systems of linear equations, matrices, determinants. Introduction to abstract vector spaces, linear transformation, inner products, geometry of Euclidean space, and eigenvalues. One quarter of college mathematics is recommended as preparation. Prerequisite(s): course 2, or placement exam score of 20 or higher. (General Education Code(s): Q.)
Score: 7.1519613 Details | Listing | Web page
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. Prerequisite(s): course 11B or 19B or 20B or AP calculus BC exam score of 4 or 5.
Score: 7.1519613 Details | Listing | Web page
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. Prerequisite(s): course 19B or 20B or AP calculus BC exam score of 4 or 5.
Score: 7.1519613 Details | Listing | Web page
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. Prerequisite(s): course 23A.
Score: 7.1519613 Details | Listing | Web page
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 Applied Mathematics and Statistics 27. Prerequisite(s): course 22 or 23A; course 21 is recommended as preparation.
Score: 7.1519613 Details | Listing | Web page
Students learn techniques of problem solving such as induction, contradiction, exhaustion, dissection, analogy, generalization, specialization, and others in the context of solving problems drawn from number theory, probability, combinatorics, graph theory, geometry, and logic. Prerequisite(s): course 11A or 19A or 20A or Math Placement Exam score of 40 or higher. B. Cooperstein
Score: 7.1519613 Details | Listing | Web page
Students learn the basic concepts and ideas necessary for upper-division mathematics and techniques of mathematical proof. Introduction to sets, relations, elementary mathematical logic, proof by contradiction, mathematical induction, and counting arguments. Prerequisite(s): courses 11A and 11B or 19A and 19B or 20A and 20B. Enrollment limited to 50.
Score: 7.1519613 Details | Listing | Web page
Complex numbers, analytic and harmonic functions, complex integration, the Cauchy integral formula, Laurent series, singularities and residues, conformal mappings. Prerequisite(s): course 23B; and either course 100 or Computer Science 101.
Score: 7.1519613 Details | Listing | Web page
The basic concepts of one-variable calculus are treated rigorously. Set theory, the real number system, numerical sequences and series, continuity, differentiation. Prerequisite(s): course 23B and either course 100 or Computer Science 101.
Score: 7.1519613 Details | Listing | Web page
Metric spaces, differentiation and integration of functions. The Riemann-Stieltjes integral. Sequences and series of functions. Prerequisite(s): course 105A.
Score: 7.1519613 Details | Listing | Web page
The Stone-Weierstrass theorem, Fourier series, differentiation and integration of functions of several variables. Prerequisite(s): course 105B.
Score: 7.1519613 Details | Listing | Web page
Linear systems, exponentials of operators, existence and uniqueness, stability of equilibria, periodic attractors, and applications. (Formerly course 106A.) Prerequisite(s): either Applied Mathematics and Statistics 27 or preferably courses 21 and 24; and either course 100 or Computer Science 101.
Score: 7.1519613 Details | Listing | Web page
Topics covered include first and second order linear partial differential equations, the heat equation, the wave equation, Laplace's equation, separation of variables, eigenvalue problems, Green's functions, Fourier series. (Formerly course 106B.) Prerequisite(s): either courses 21 and 24 or Applied Mathematics and Statistics 27; and either course 100 or Computer Science 101; course 106 is recommended as preparation.
Score: 7.1519613 Details | Listing | Web page
Prime numbers, unique factorization, congruences with applications (e.g., to magic squares). Rational and irrational numbers. Continued fractions. Introduction to Diophantine equations. An introduction to some of the ideas and outstanding problems of modern mathematics. Prerequisite(s): course 100 or Computer Science 101. (General Education Code(s): Q.)
Score: 7.1519613 Details | Listing | Web page
Group theory including the Sylow theorem, the structure of abelian groups, and permutation groups. Prerequisite(s): course 21 or Applied Mathematics and Statistics 27 and either course 100 or Computer Science 101.
Score: 7.1519613 Details | Listing | Web page