| source UC San Diego (X) |
level |
department Mathematics (X) |
Functions and their graphs. Linear and polynomial functions, zeroes, inverse functions, exponential and logarithmic, trigonometric functions and their inverses. Emphasis on understanding algebraic, numerical and graphical approaches making use of graphing calculators. (No credit given if taken after Math. 4C, 1A/10A, or 2A/20A.) Three or more years of high school mathematics or equivalent recommended.
Score: 7.043127 Details | Listing | Web page
Review of polynomials. Graphing functions and relations: graphing rational functions, effects of linear changes of coordinates. Circular functions and right triangle trigonometry. Reinforcement of function concept: exponential, logarithmic, and trigonometric functions. Vectors. Conic sections. Polar coordinates. Three lectures, one recitation. (No credit given if taken after Math. 1A/10A or 2A/20A. Two units of credit given if taken after Math. 3C.)
Score: 7.043127 Details | Listing | Web page
Differentiation and integration of algebraic functions. Fundamental theorem of calculus. Applications. (No credit given if taken after Math. 20A).
Score: 7.043127 Details | Listing | Web page
Further applications of the definite integral. Calculus of trigonometric, logarithmic, and exponential functions. Complex numbers. (No credit given if taken after Math. 2B/20B. Formerly numbered Math. 1B.)
Score: 7.043127 Details | Listing | Web page
Vector geometry, velocity, and acceleration vectors. (No credit given if taken after Math. 2C/20C. Formerly numbered Math. 1C.)
Score: 7.043127 Details | Listing | Web page
Events and probabilities, conditional probability, Bayes formula. Discrete random variables: mean, variance; binomial, Poisson distributions. Continuous random variables: densities, mean, variance; normal, uniform, exponential distributions. Sample statistics, confidence intervals, hypothesis testing, regression. Applications. Intended for biology and social science majors.
Score: 7.043127 Details | Listing | Web page
Introduction to the use of software in probabilistic and statistical analysis. Emphasis on understanding connections between the theory of probability and statistics, numerical results of real data, and learning techniques of data analysis and interpretation useful for solving scientific problems.
Score: 7.043127 Details | Listing | Web page
Basic discrete mathematical structures: sets, relations, functions, sequences, equivalence relations, partial orders, number systems. Methods of reasoning and proofs: propositional logic, predicate logic, induction, recursion, pigeonhole principle. Infinite sets and diagonalization. Basic counting techniques; permutations and combinations. Applications will be given to digital logic design, elementary number theory, design of programs, and proofs of program correctness. Equivalent to CSE 20. Credit not offered for both Math. 15A and CSE 20.
Score: 7.043127 Details | Listing | Web page
This course introduces mathematical tools for the qualitative and quantitative analysis of algorithms and computer systems. Topics to be covered include basic enumeration and counting techniques; recurrence relations; graph theory; asymptotic notation; elementary applied discrete probability. Equivalent to CSE 21. Credit not offered for both Math. 15B and CSE 21.
Score: 7.043127 Details | Listing | Web page
Foundations of differential and integral calculus of one variable. Functions, graphs, continuity, limits, derivative, tangent line. Applications with algebraic, exponential, logarithmic, and trigonometric functions. Introduction to the integral. (Two credits given if taken after Math. 1A/10A and no credit given if taken after Math. 1B/10B or Math. 1C/10C. Formerly numbered Math. 2A.)
Score: 7.043127 Details | Listing | Web page
Integral calculus of one variable and its applications, with exponential, logarithmic, hyperbolic, and trigonometric functions. Methods of integration. Infinite series. Polar coordinates in the plane and complex exponentials. (Two units of credits given if taken after Math. 1B/10B or Math. 1C/10C.)
Score: 7.043127 Details | Listing | Web page
Vector geometry, vector functions and their derivatives. Partial differentiation. Maxima and minima. Double integration, Two units of credit given if taken after Math. 10C. Credit not offered for both Math. 20C and 31BH. Formerly numbered Math. 21C.
Score: 7.043127 Details | Listing | Web page
Ordinary differential equations: exact, separable, and linear; constant coefficients, undetermined coefficients, variations of parameters. Systems. Series solutions. Laplace transforms. Techniques for engineering sciences. Computing symbolic and graphical solutions using Matlab. Formerly numbered Math. 21D. May be taken as repeat credit for Math. 21D.
Score: 7.043127 Details | Listing | Web page
Change of variable in multiple integrals, Jacobian, Line integrals, Green’s theorem. Vector fields, gradient fields, divergence, curl. Spherical/cylindrical coordinates. Taylor series in several variables. Surface integrals, Stoke’s theorem. Gauss’ theorem. Conservative fields. Credit not offered for both Math. 20E and 31CH.
Score: 7.043127 Details | Listing | Web page
Matrix algebra, Gaussian elimination, determinants. Linear and affine subspaces, bases of Euclidean spaces. Eigenvalues and eigenvectors, quadratic forms, orthogonal matrices, diagonalization of symmetric matrices. Applications. Computing symbolic and graphical solutions using Matlab. Credit not offered for both Math. 20F and 31AH.
Score: 7.043127 Details | Listing | Web page
First quarter of three-quarter honors integrated linear algebra/multivariable calculus sequence for well-prepared students. Topics include: real/complex number systems, vector spaces, linear transformations, bases and dimension, change of basis, eigenvalues, eigenvectors, diagonalization. Credit not offered for both Math. 31AH and 20F.
Score: 7.043127 Details | Listing | Web page
Second quarter of three-quarter honors integrated linear algebra/multivariable calculus sequence for well-prepared students. Topics include: derivative in several variables, Jacobian matrices, extrema and constrained extrema, integration in several variables. Credit not offered for both Math. 31BH and 20C.
Score: 7.043127 Details | Listing | Web page
Third quarter of honors integrated linear algebra/multivariable calculus sequence for well-prepared students. Topics include: change of variables formula, integration of differential forms, exterior derivative, generalized Stoke’s theorem, conservative vector fields, potentials. Credit not offered for both Math. 31CH and 20E.
Score: 7.043127 Details | Listing | Web page
The Freshman Seminar Program is designed to provide new students with the opportunity to explore an intellectual topic with a faculty member in a small seminar setting. Freshman seminars are offered in all campus departments and undergraduate colleges, and topics vary from quarter to quarter. Enrollment is limited to 15 to 20 students, with preference given to entering freshman.
Score: 7.043127 Details | Listing | Web page
(Cross-listed with EDS 30) Revisit students’ learning difficulties in mathematics in more depth to prepare students to make meaningful observations of how K-12 teachers deal with these difficulties. Explore how instruction can use students’ knowledge to pose problems that stimulate students’ intellectual curiosity.
Score: 7.043127 Details | Listing | Web page
Independent study or research under direction of a member of the faculty.
Score: 7.043127 Details | Listing | Web page
First course in a rigorous three-quarter introduction to the methods and basic structures of higher algebra. Topics include: groups, subgroups and factor groups, homomorphisms, rings, fields. Students may not receive credit for both Math. 100A and Math. 103A.
Score: 7.043127 Details | Listing | Web page
Second course in a rigorous three-quarter introduction to the methods and basic structures of higher algebra. Topics include: rings (especially polynomial rings) and ideals, unique factorization, fields; linear algebra from perspective of linear transformations on vector spaces, including inner product spaces, determinants, diagonalization. Students may not receive credit for both Math. 100B and Math. 103B.
Score: 7.043127 Details | Listing | Web page
Third course in a rigorous three-quarter introduction to the methods and basic structures of higher algebra. Topics include: linear transformations, including Jordan canonical form and rational canonical form; Galois theory, including the insolvability of the quintic.
Score: 7.043127 Details | Listing | Web page
A second course in linear algebra from a computational yet geometric point of view. Elementary Hermitian matrices, Schur’s theorem, normal matrices, and quadratic forms. Moore-Penrose generalized inverse and least square problems. Vector and matrix norms. Characteristic and singular values. Canonical forms. Determinants and multilinear algebra. Three lectures, one recitation.
Score: 7.043127 Details | Listing | Web page
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