(Conjoined with MATH 174.) (Credit not allowed for both MATH 171A and ECON 172A.) May be repeated for credit with consent of adviser as topics vary. The course will incorporate talks by experts from industry and students will be helped to carry out independent projects. May be taken for credit nine times. Error analysis of numerical methods for eigenvalue problems and singular value problems. In recent years, topics have included Markov processes, martingale theory, stochastic processes, stationary and Gaussian processes, ergodic theory. May be coscheduled with MATH 212A. Cauchys formula. Preconditioned conjugate gradients. Prerequisites: MATH 181B or consent of instructor. Non-linear first order equations, including Hamilton-Jacobi theory. Vector and matrix norms. MATH 160B. Non-linear first order equations, including Hamilton-Jacobi theory. Nongraduate students may enroll with consent of instructor. Data Science (28 units): COGS 9, DSC 10, DSC 20, DSC 30, DSC 40A-B, DSC 80. Some scientific programming experience is recommended. Prerequisites: graduate standing or consent of instructor. In recent years, topics have included Riemannian geometry, Ricci flow, and geometric evolution. Students who have not taken MATH 200C may enroll with consent of instructor. Third course in graduate partial differential equations. Prerequisites: MATH 120A or consent of instructor. Introduction to Differential Equations (4). Three or more years of high school mathematics or equivalent recommended. Techniques for engineering sciences. So med schools really want students to take Statistics. MATH 199. Prerequisites: MATH 174 or MATH 274, or consent of instructor. (S/U grade only. Hierarchical basis methods. Introduction to Mathematical Biology II (4). (S/U grades permitted. Prerequisites: MATH 100B or MATH 103B. Prerequisites: MATH 200B. Integral calculus of one variable and its applications, with exponential, logarithmic, hyperbolic, and trigonometric functions. Antiderivatives, definite integrals, the Fundamental Theorem of Calculus, methods of integration, areas and volumes, separable differential equations. Optimization Methods for Data Science II (4). MATH 206A. Locally compact Hausdorff spaces, Banach and Hilbert spaces, linear functionals. Generalized linear models, including logistic regression. Introduction to varied topics in several complex variables. Prerequisites: consent of adviser. Prerequisites: MATH 18 or MATH 20F or MATH 31AH and MATH 20D. Students who have not completed listed prerequisites may enroll with consent of instructor. Linear and affine subspaces, bases of Euclidean spaces. Posets and Sperner property. Prerequisites: admission to the Honors Program in mathematics, department stamp. An introduction to ordinary differential equations from the dynamical systems perspective. (S/U grade only.). Medicine (M.D.) Review of polynomials. Prerequisites: MATH 190 or consent of instructor. Topics include groups, subgroups and factor groups, homomorphisms, rings, fields. Numerical Approximation and Nonlinear Equations (4). Advanced Techniques in Computational Mathematics I (4). Vector spaces, orthonormal bases, linear operators and matrices, eigenvalues and diagonalization, least squares approximation, infinite-dimensional spaces, completeness, integral equations, spectral theory, Greens functions, distributions, Fourier transform. Prerequisites: MATH 240C, students who have not completed MATH 240C may enroll with consent of instructor. Examples. The Department of Mathematics offers graduate programs leading to the MA (pure or applied mathematics), MS (statistics), and PhD degrees. Prerequisites: MATH 202B or consent of instructor. Introduction to Discrete Mathematics (4). Develop teachers knowledge base (knowledge of mathematics content, pedagogy, and student learning) in the context of advanced mathematics. Lax-Milgram Theorem and LBB stability. Introduction to varied topics in combinatorial mathematics. MATH 261A must be taken before MATH 261B. Computer Science for K-12 Educators. Letters of support from potential faculty advisors are encouraged. Offers conceptual explanation of techniques, along with opportunities to examine, implement, and practice them in real and simulated data. Prior or concurrent enrollment in MATH 109 is highly recommended. (Students may not receive credit for both MATH 100B and MATH 103B.) (Students may not receive credit for both MATH 100A and MATH 103A.) Topics in Algebraic Geometry (4). Probability & Statistics B.S. Double integration. Data provided by the Association of American Medical Colleges (AAMC). Lie groups and algebras, connections in bundles, homotopy sequence of a bundle, Chern classes. May be repeated for credit with consent of adviser as topics vary. If MATH 184 and MATH 188 are concurrently taken, credit only offered for MATH 188. Basic iterative methods. Project-oriented; projects designed around problems of current interest in science, mathematics, and engineering. Statistics can be used to draw conclusions about data and provides a foundation for more sophisticated data analysis techniques. Textbook:None. Please consult the Department of Mathematics to determine the actual course offerings each year. Seminar in Differential Geometry (1), Various topics in differential geometry. Statistics is used in many areas of scientific and social research, is critical to business and manufacturing, and provides the mathematical foundation for machine learning and data mining. Extracurricular Industry Practicum (2 or 4). (Two units of credit offered for MATH 180A if ECON 120A previously, no credit offered if ECON 120A concurrently. Transferring from the Master's program may require renewal of an I-20 for international students, and such students should make their financial plans accordingly. ), Diagnostics, outlier detection, robust regression. (S/U grades only. Probabilistic Combinatorics and Algorithms II (4). Topics include analysis on graphs, random walks and diffusion geometry for uniform and non-uniform sampling, eigenvector perturbation, multi-scale analysis of data, concentration of measure phenomenon, binary embeddings, quantization, topic modeling, and geometric machine learning, as well as scientific applications. Topics include unique factorization, irrational numbers, residue systems, congruences, primitive roots, reciprocity laws, quadratic forms, arithmetic functions, partitions, Diophantine equations, distribution of primes. Prerequisites: MATH 20C or MATH 31BH and MATH 18 or 20F or 31AH. Selected topics from integer programming, network flows, transportation problems, inventory problems, and other applications. Graduate students will do an extra paper, project, or presentation, per instructor. This encompasses many methods such as dimensionality reduction, sparse representations, variable selection, classification, boosting, bagging, support vector machines, and machine learning. (S/U grade only. Topics include differentiation of functions of several real variables, the implicit and inverse function theorems, the Lebesgue integral, infinite-dimensional normed spaces. Introduction to Numerical Analysis: Linear Algebra (4). (Two credits given if taken after MATH 1A/10A and no credit given if taken after MATH 1B/10B or MATH 1C/10C. A rigorous introduction to algebraic combinatorics. The Enigma. Extremal Combinatorics and Graph Theory (4). Cauchy theorem and its applications, calculus of residues, expansions of analytic functions, analytic continuation, conformal mapping and Riemann mapping theorem, harmonic functions. Prerequisites: MATH 270A or consent of instructor. Partial Differential Equations III (4). There are no sections of this course currently scheduled. Students who have not completed MATH 231B may enroll with consent of instructor. The mathematical modeling aspect of statistics is profound - it is what we humans Prerequisites: MATH 237A. Students who have not completed listed prerequisites may enroll with consent of instructor. Prerequisites: MATH 260A or consent of instructor. Multivariate time series. Hypothesis testing, including analysis of variance, and confidence intervals. Stationary processes and their spectral representation. (Students may not receive credit for both MATH 140A and MATH 142A.) Prerequisites: graduate standing or consent of instructor. MATH 160A. May be taken for credit six times with consent of adviser as topics vary. Linear and polynomial functions, zeroes, inverse functions, exponential and logarithmic, trigonometric functions and their inverses. May be taken for credit three times with consent of adviser as topics vary. Polar coordinates in the plane and complex exponentials. Prerequisites: graduate standing. Prerequisites: graduate standing. Fourier analysis of functions and distributions in several variables. Calculus of functions of several variables, inverse function theorem. Prerequisites: graduate standing or consent of instructor. Continued development of a topic in topology. The R programming language is one of the most widely-used tools for data analysis and statistical programming. Prerequisites: graduate standing. Numerical Ordinary Differential Equations (4). A priori error estimates. MATH 174. Students who have not completed listed prerequisites may enroll with consent of instructor. Classical cryptanalysis. Topics will vary from year to year in areas of mathematics and their development. Groups, rings, linear algebra, rational and Jordan forms, unitary and Hermitian matrices, matrix decompositions, perturbation of eigenvalues, group representations, symmetric functions, fast Fourier transform, commutative algebra, Grobner basis, finite fields. MATH 2. Explore Courses & Programs Languages and English Learning Languages and English Learning Topics include differential equations, dynamical systems, and probability theory applied to a selection of biological problems from population dynamics, biochemical reactions, biological oscillators, gene regulation, molecular interactions, and cellular function. Teaching Assistant Training (2 or 4), A course in which teaching assistants are aided in learning proper teaching methods through faculty-led discussions, preparation and grading of examinations and other written exercises, academic integrity, and student interactions. Prerequisites: graduate standing. Interpolation. Prerequisites: MATH 103A or MATH 100A or consent of instructor. Other topics if time permits. Students who have not completed the listed prerequisite(s) may enroll with consent of instructor. Change of variable in multiple integrals, Jacobian, Line integrals, Greens theorem. Topics in Combinatorial Mathematics (4). Workload credit onlynot for baccalaureate credit. Seminar in Computational and Applied Mathematics (1), Various topics in computational and applied mathematics. All courses, faculty listings, and curricular and degree requirements described herein are subject to change or deletion without notice. Prerequisites: MATH 200 and 250 or consent of instructor. Integral calculus of functions of one variable, with applications. MATH 237B. May be coscheduled with MATH 112A. Instructor may choose further topics such as Urysohns lemma, Urysohns metrization theorem. Credit not offered for MATH 158 if MATH 154 was previously taken. Students who have not completed listed prerequisites may enroll with consent of instructor. Turing machines. Bivariate and more general multivariate normal distribution. Numerical Analysis in Multiscale Biology (4). Students should have exposure to one of the following programming languages: C, C++, Java, Python, R. Prerequisites: MATH 18 or MATH 20F or MATH 31AH and one of BILD 62, COGS 18 or CSE 5A or CSE 6R or CSE 8A or CSE 11 or DSC 10 or ECE 15 or ECE 143 or MATH 189. Topics include graph visualization, labelling, and embeddings, random graphs and randomized algorithms. Optimality conditions; linear and quadratic programming; interior methods; penalty and barrier function methods; sequential quadratic programming methods. Students who have not taken MATH 200C may enroll with consent of instructor. Prerequisites: MATH 31CH or MATH 109 or consent of instructor. Optimization Methods for Data Science I (4). Lebesgue spaces and interpolation, elements of Fourier analysis and distribution theory. This course will cover discrete and random variables, data analysis and inferential statistics, likelihood estimators and scoring matrices with applications to biological problems. (No credit given if taken after or concurrent with MATH 20A.) Nongraduate students may enroll with consent of instructor. (Credit not offered for MATH 183 if ECON 120A, ECE 109, MAE 108, MATH 181A, or MATH 186 previously or concurrently taken. Prerequisites: MATH 212A and graduate standing. Recommended preparation: course work in linear algebra and real analysis. This course is intended as both a refresher course and as a first course in the applications of statistical thinking and methods. Locally convex spaces, weak topologies. (Two units of credits given if taken after MATH 1B/10B or MATH 1C/10C.) MATH 256. Caesar-Vigenere-Playfair-Hill substitutions. About Us. Time dependent (parabolic and hyperbolic) PDEs. Random walk, Poisson process. Lagrange inversion, exponential structures, combinatorial species. MATH 190B. Optimality conditions, strong duality and the primal function, conjugate functions, Fenchel duality theorems, dual derivatives and subgradients, subgradient methods, cutting plane methods. MATH 210B. MATH 182. Introduction to the integral. Topics covered in the sequence include the measure-theoretic foundations of probability theory, independence, the Law of Large Numbers, convergence in distribution, the Central Limit Theorem, conditional expectation, martingales, Markov processes, and Brownian motion. Third course in algebraic geometry. Prerequisites: MATH 31BH with a grade of B or better, or consent of instructor. Applications to approximation algorithms, distributed algorithms, online and parallel algorithms. (S/U grades permitted. upcoming events and courses, Computer-Aided Design (CAD) & Building Information Modeling (BIM), Teaching English as a Foreign Language (TEFL), Global Environmental Leadership and Sustainability, System Administration, Networking and Security, Burke Lectureship on Religion and Society, California Workforce and Degree Completion Needs, UC Professional Development Institute (UCPDI), Workforce Innovation Opportunity Act (WIOA), Discrete Math: Problem Solving for Engineering, Programming, & Science, Probability and Statistics for Deep Learning, Describe the relation between two variables, Work with sample data to make inferences about the data. Sobolev spaces and initial/boundary value problems for linear elliptic, parabolic, and hyperbolic equations. Completion of MATH 102 is encouraged but not required. Further Topics in Differential Geometry (4). A rigorous introduction to systems of ordinary differential equations. Synchronous attendance is NOT required.You will have access to your online course on the published start date OR 1 business day after your enrollment is confirmed if you enroll on or after the published start date. Markov Chains and Random walks. Independent reading in advanced mathematics by individual students. (This program is offered only under the Comprehensive Examination Plan.). Nongraduate students may enroll with consent of instructor. Students who have not completed listed prerequisites may enroll with consent of instructor. The emphasis is on semiparametric inference, and material is drawn from recent literature. Applications of the residue theorem. Further Topics in Probability and Statistics (4). Random vectors, multivariate densities, covariance matrix, multivariate normal distribution. Second course in linear algebra from a computational yet geometric point of view. The one-time system. Elementary Mathematical Logic I (4). Fourier transformations. This course is designed for prospective secondary school mathematics teachers. Basic counting techniques; permutation and combinations. Prerequisites: MATH 216B. ), MATH 500. Software: Students will use MyStatLab and StatCrunch to complete assignments. Hypothesis testing, type I and type II errors, power, one-sample t-test. Further topics may include exterior differential forms, Stokes theorem, manifolds, Sards theorem, elements of differential topology, singularities of maps, catastrophes, further topics in differential geometry, topics in geometry of physics. Examples of all the above. The Graduate Program. Locally compact Hausdorff spaces, Banach and Hilbert spaces, linear functionals. Laplace, heat, and wave equations. Linear programming, the simplex method, duality. Courses: 4. This is the second course in a three-course sequence in mathematical methods in data science. Graduate students do an extra paper, project, or presentation, per instructor. This multimodality course will focus on several topics of study designed to develop conceptual understanding and mathematical relevance: linear relationships; exponents and polynomials; rational expressions and equations; models of quadratic and polynomial functions and radical equations; exponential and logarithmic functions; and geometry and trigonometry. MATH 267B. Prerequisites: graduate standing. Recommended preparation: completion of undergraduate probability theory (equivalent to MATH 180A) highly recommended. Introduction to Computational Stochastics (4). ), MATH 259A-B-C. Geometrical Physics (4-4-4). Convex optimization problems, linear matrix inequalities, second-order cone programming, semidefinite programming, sum of squares of polynomials, positive polynomials, distance geometry. Urysohns lemma, Urysohns metrization theorem DSC 10, DSC 20, DSC 20, DSC 10 DSC! In data Science and barrier function methods ; sequential quadratic programming methods assignments... 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