Mathematics
151 courses · UC Irvine · 2026-2027 Catalog
Classes: Fall 2026
MATH 1A Pre-Calculus I
- Units
- 0
Basic equations and inequalities, linear and quadratic functions, and systems of simultaneous equations.
MATH 1B Pre-Calculus II
- Units
- 4
- Prerequisite
- Recommended: A passing score on the Pre-Calculus Self-Assessment exam, or a score of 450 or higher on the Mathematics section of the SAT Reasoning Test. Not for students with a score of 3 or higher on the AP Calc AB exam. Not for students with a score of 3 or higher on the AP Calc BC exam
Preparation for calculus and other mathematics courses. Exponentials, logarithms, trigonometry, polynomials, and rational functions. Satisfies no requirements other than contribution to the 180 units required for graduation.
MATH 2A Single-Variable Calculus I
- Units
- 4
- Prerequisite
- MATH 1B with a minimum grade of C- or SAT Mathematics with a minimum score of 650 or ACT Mathematics with a minimum score of 29. Placement via the Calculus Placement exam (fee required) is also accepted
Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.
MATH 2AX Calculus Preparation
- Units
- 1
- Corequisite
- MATH 2A
Group activities designed to review and reinforce fundamental concepts essential for success in Calculus. Linear functions, quadratic functions, polynomials, and rational functions; exponentials and logarithms; trigonometry; absolute values. Graphs of functions.
MATH 2B Single-Variable Calculus II
- Units
- 4
- Prerequisite
- MATH 2A or MATH 5A or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3 or AP Calculus AB Subscore with a minimum score of 3
Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series.
MATH 2BX Calculus Preparation II
- Units
- 1
- Corequisite
- MATH 2B
Group activities designed to review and reinforce fundamental concepts essential for success in integral calculus. Differentiation and integration techniques, review of trigonometric functions, sequences and series, Taylor and power series. To be taken concurrently with MATH 2B.
MATH 2D Multivariable Calculus I
- Units
- 4
- Prerequisite
- MATH 2B or MATH 5B or AP Calculus BC with a minimum score of 4
Differential and integral calculus of real-valued functions of several real variables, including applications. Polar coordinates.
MATH 2E Multivariable Calculus II
- Units
- 4
- Prerequisite
- MATH 2D
The differential and integral calculus of vector-valued functions. Implicit and inverse function theorems. Line and surface integrals, divergence and curl, theorems of Greens, Gauss, and Stokes.
MATH 3A Introduction to Linear Algebra
- Units
- 4
- Prerequisite
- MATH 2B or MATH 5B or AP Calculus BC with a minimum score of 4
Systems of linear equations, matrix operations, determinants, eigenvalues and eigenvectors, vector spaces, subspaces, and dimension.
MATH 3D Elementary Differential Equations
- Units
- 4
- Prerequisite
- MATH 3A and MATH 2D
Linear differential equations, variation of parameters, constant coefficient cookbook, systems of equations, Laplace transforms, series solutions.
MATH 5A Calculus for Life Sciences I
- Units
- 4
- Prerequisite
- MATH 1B with a minimum grade of C- or SAT Mathematics with a minimum score of 650 or ACT Mathematics with a minimum score of 29. Placement via the Calculus Placement exam (fee required) is also accepted
Differential calculus with applications to life sciences. Exponential, logarithmic, and trigonometric functions. Limits, differentiation techniques, optimization and difference equations.
MATH 5B Calculus for Life Sciences II
- Units
- 4
- Prerequisite
- MATH 5A or MATH 2A or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3 or AP Calculus AB Subscore with a minimum score of 3
Integral calculus and multivariable calculus with applications to life sciences. Integration techniques, applications of the integral, phase plane methods and basic modeling, basic multivariable methods.
MATH 8 Explorations in Functions and Modeling
- Units
- 4
- Prerequisite
- MATH 2A or MATH 5A or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3
- Corequisite
- MATH 2A or MATH 5A
Explorations of applications and connections in topics in algebra, geometry, calculus, and statistics for future secondary math educators. Emphasis on nonstandard modeling problems.
MATH 9 Introduction to Programming for Numerical Analysis
- Units
- 4
- Prerequisite
- MATH 2A or MATH 5A or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3 or AP Calculus AB Subscore with a minimum score of 3
Introduction to computers and programming using Matlab and Python. Representation of numbers and precision, input/output, functions, custom data types, testing/debugging, reading exceptions, plotting data, numerical differentiation, basics of algorithms. Analysis of random processes using computer simulations.
MATH 10 Introduction to Programming for Data Science
- Units
- 4
- Prerequisite
- MATH 2D and MATH 3A and MATH 9
- Corequisite
- MATH 2D and MATH 3A
Introduction to Python for data science. Selecting appropriate data types; functions and methods; plotting; the libraries NumPy, pandas, scikit-learn. Foundations of machine learning.
MATH 13 Introduction to Abstract Mathematics
- Units
- 4
- Prerequisite
- MATH 2A or MATH 5A or I&C SCI 6D or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3 or AP Calculus AB Subscore with a minimum score of 3
Introduction to formal definition and rigorous proof writing in mathematics. Topics include basic logic, set theory, equivalence relations, and various proof techniques such as direct, induction, contradiction, contrapositive, and exhaustion.
MATH 13X Skills for Success in Abstract Math
- Units
- 1
- Corequisite
- MATH 13
Group activities designed to practice fundamental concepts used in abstract mathematics. Logic and reasoning; functions; sets. Proof techniques. Most coursework is done in class in collaboration with peers.
MATH 99 New Math Major Seminar for First-Year and Transfer Students
- Units
- 1
A series of presentations and activities to help first-year and transfer students transition to the UCI mathematics majors. Presentations are given by faculty, current students, and school staff to ensure that students make the most of the math major.
MATH 105A Numerical Analysis I
- Units
- 4
- Prerequisite
- MATH 3A and MATH 9
- Corequisite
- MATH 105LA
Introduction to the theory and practice of numerical computation with an emphasis on solving equations. Solving transcendental equations; linear systems, Gaussian elimination, QR factorization, iterative methods, eigenvalue computation, power method.
MATH 105B Numerical Analysis II
- Units
- 4
- Prerequisite
- MATH 105A
- Corequisite
- MATH 105LB
Introduction to the theory and practice of numerical computation with an emphasis on topics from calculus and approximation theory. Lagrange interpolation; Gaussian quadrature; Fourier series and transforms; Methods from data science including least squares and L1 regression.
MATH 105LA Numerical Analysis Laboratory
- Units
- 1
- Corequisite
- MATH 105A
Provides practical experience to complement the theory developed in MATH 105A.
MATH 105LB Numerical Analysis Laboratory
- Units
- 1
- Corequisite
- MATH 105B
Provides practical experience to complement the theory developed in MATH 105B.
MATH 107 Numerical Differential Equations
- Units
- 4
- Prerequisite
- MATH 3D and MATH 105B
- Corequisite
- MATH 107L
Theory and applications of numerical methods to initial and boundary-value problems for ordinary and partial differential equations.
MATH 107L Numerical Differential Equations Laboratory
- Units
- 1
- Corequisite
- MATH 107
Provides practical experience to complement the theory developed in MATH 107.
MATH 110A Optimization I
- Units
- 4
- Prerequisite
- MATH 2D and MATH 10 and MATH 121B
- Corequisite
- MATH 121B
Introduction to optimization, linear search method, trust region method, Newton method, linear programming, linear, and non-linear least square methods.
MATH 110B Optimization II
- Units
- 4
- Prerequisite
- MATH 110A with a minimum grade of C-
The simplex method, interior point method, penalty barrier method, primal dual method, augmented Lagrangian method, and stochastic gradient method.
MATH 112A Introduction to Partial Differential Equations and Applications I
- Units
- 4
- Prerequisite
- MATH 2E and MATH 3D
Introduction to ordinary and partial differential equations and their applications in engineering and science. Basic methods for classical PDEs (potential, heat, and wave equations). Classification of PDEs, separation of variables and series expansions, special functions, eigenvalue problems.
MATH 112B Introduction to Partial Differential Equations and Applications II
- Units
- 4
- Prerequisite
- MATH 112A
Introduction to partial differential equations and their applications in engineering and science. Basic methods for classical PDEs (potential, heat, and wave equations). Green functions and integral representations, method of characteristics.
MATH 112C Introduction to Partial Differential Equations and Applications III
- Units
- 4
- Prerequisite
- MATH 112B
Nonhomogeneous problems and Green's functions, Sturm-Liouville theory, general Fourier expansions, applications of partial differential equations in different areas of science.
MATH 113A Mathematical Modeling in Biology I
- Units
- 4
- Prerequisite
- MATH 2B or MATH 5B or AP Calculus BC with a minimum score of 4
Discrete mathematical and statistical models; difference equations, population dynamics, Markov chains, and statistical models in biology.
MATH 113B Mathematical Modeling in Biology II
- Units
- 4
- Prerequisite
- MATH 113A
Linear algebra; differential equations models; dynamical systems; stability; hysteresis; phase plane analysis; applications to cell biology, viral dynamics, and infectious diseases.
MATH 115 Mathematical Modeling
- Units
- 4
- Prerequisite
- MATH 112A
Mathematical modeling and analysis of phenomena that arise in engineering physical sciences, biology, economics, or social sciences.
MATH 117 Dynamical Systems
- Units
- 4
- Prerequisite
- MATH 3D and MATH 140A
Introduction to the modern theory of dynamical systems including contraction mapping principle, fractals and chaos, conservative systems, Kepler problem, billiard models, expanding maps, Smale's horseshoe, topological entropy.
MATH 118 The Theory of Differential Equations
- Units
- 4
- Prerequisite
- MATH 3D and MATH 140A
Existence and uniqueness of solutions, continuous dependence of solutions on initial conditions and parameters, Lyapunov and asymptotic stability, Floquet theory, nonlinear systems, and bifurcations.
MATH 120A Introduction to Abstract Algebra: Groups
- Units
- 4
- Prerequisite
- MATH 3A and MATH 13 with a minimum grade of C-
Axioms for group theory; permutation groups, matrix groups. Isomorphisms, homomorphisms, quotient groups. Advanced topics as time permits. Special emphasis on doing proofs.
MATH 120B Introduction to Abstract Algebra: Rings and Fields
- Units
- 4
- Prerequisite
- MATH 120A with a minimum grade of C-
Basic properties of rings; ideals, quotient rings; polynomial and matrix rings. Elements of field theory.
MATH 120C Introduction to Abstract Algebra: Galois Theory
- Units
- 4
- Prerequisite
- MATH 120B
Galois Theory: proof of the impossibility of certain ruler-and-compass constructions (squaring the circle, trisecting angles); nonexistence of analogues to the "quadratic formula" for polynomial equations of degree 5 or higher.
MATH 121A Linear Algebra I
- Units
- 4
- Prerequisite
- MATH 3A and MATH 13 with a minimum grade of C-
Introduction to modern abstract linear algebra. Special emphasis on students doing proofs. Vector spaces, linear independence, bases, dimension. Linear transformations and their matrix representations. Theory of determinants.
MATH 121B Linear Algebra II
- Units
- 4
- Prerequisite
- MATH 121A with a minimum grade of C-
Introduction to modern abstract linear algebra. Special emphasis on students doing proofs. Inner products; similarity of matrices; singular value decomposition. Other topics as time permits.
MATH 130A Probability I
- Units
- 4
- Prerequisite
- MATH 3A
Combinatorial probability, conditional probabilities, independence, discrete and continuous random variables, expectation and variance, common probability distributions.
MATH 130B Probability II
- Units
- 4
- Prerequisite
- MATH 130A or STATS 120A
Joint distributions, sums of independent random variables, conditional distributions and conditional expectation, covariances, moment generating functions, limit theorems.
MATH 130C Stochastic Processes
- Units
- 4
- Prerequisite
- MATH 130B
Markov chains, Brownian motion, Gaussian processes, applications to option pricing and Markov chain Monte Carlo methods.
MATH 134A Fixed Income
- Units
- 4
- Prerequisite
- MATH 130A or STATS 120A
Overview of interest theory, time value of money, annuities/cash flows with payments that are not contingent, loans, sinking funds, bonds, general cash flow and portfolios, immunization, duration and convexity, swaps.
MATH 134B Mathematics of Financial Derivatives
- Units
- 4
- Prerequisite
- MATH 130A with a minimum grade of C-
General derivatives; call/put options; hedging and investment strategies; spreads and collars; risk management; forwards and futures; bonds.
MATH 134C Mathematical Models for Finance
- Units
- 4
- Prerequisite
- MATH 134B
General properties of options: option contracts (call and put options, European, American and exotic options); binomial option pricing model, Black-Scholes option pricing model; risk-neutral pricing formula using Monte-Carlo simulation; option greeks and risk management; interest rate derivatives, Markowitz portfolio theory.
MATH 140A Elementary Analysis I
- Units
- 4
- Prerequisite
- MATH 2D and MATH 3A and MATH 13 with a minimum grade of C-
Introduction to real analysis, including convergence of sequence, infinite series, differentiation and integration, and sequences of functions. Students are expected to do proofs.
MATH 140B Elementary Analysis II
- Units
- 4
- Prerequisite
- MATH 140A with a minimum grade of C-
Introduction to real analysis including convergence of sequences, infinite series, differentiation and integration, and sequences of functions. Students are expected to do proofs.
MATH 140C Analysis in Several Variables
- Units
- 4
- Prerequisite
- MATH 140B
Rigorous treatment of multivariable differential calculus. Jacobians, Inverse and Implicit Function theorems.
MATH H140A Honors Introduction to Graduate Analysis I
- Units
- 5
- Prerequisite
- MATH 2E with a minimum grade of A and MATH 3A and MATH 13 with a minimum grade of A and MATH 121A with a minimum grade of A and MATH 140A with a minimum grade of A
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
MATH H140B Honors Introduction to Graduate Analysis II
- Units
- 5
- Prerequisite
- MATH H140A with a minimum grade of C-
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
MATH H140C Honors Introduction to Graduate Analysis III
- Units
- 5
- Prerequisite
- MATH H140B with a minimum grade of C-
Construction of the real number system; topology of the real line; concepts of continuity, differential, and integral calculus; sequences and series of functions, equicontinuity, metric spaces, multivariable differential, and integral calculus; implicit functions, curves and surfaces.
MATH 141 Introduction to Topology
- Units
- 4
- Prerequisite
- MATH 140A
The elements of naive set theory and the basic properties of metric spaces. Introduction to topological properties.
MATH 147 Complex Analysis
- Units
- 4
- Prerequisite
- MATH 140B (may be taken concurrently)
Rigorous treatment of basic complex analysis: analytic functions, Cauchy integral theory and its consequences, power series, residue calculus, harmonic functions, conformal mapping. Students are expected to do proofs.
MATH 150 Introduction to Mathematical Logic
- Units
- 4
- Prerequisite
- MATH 13 with a minimum grade of C- or (I&C SCI 6B with a minimum grade of C- and I&C SCI 6D with a minimum grade of C-)
First order logic through the Completeness Theorem for predicate logic.
MATH 161 Modern Geometry
- Units
- 4
- Prerequisite
- MATH 13 with a minimum grade of C- or (I&C SCI 6B with a minimum grade of C- and I&C SCI 6D with a minimum grade of C-)
Euclidean Geometry; Hilbert's Axioms; Absolute Geometry; Hyperbolic Geometry; the Poincare Models; and Geometric Transformations.
MATH 162A Introduction to Differential Geometry I
- Units
- 4
- Prerequisite
- MATH 2E and MATH 3D
Applications of advanced calculus and linear algebra to the geometry of curves and surfaces in space.
MATH 162B Introduction to Differential Geometry II
- Units
- 4
- Prerequisite
- MATH 162A with a minimum grade of C-
Applications of advanced calculus and linear algebra to the geometry of curves and surfaces in space.
MATH 173A Introduction to Cryptology I
- Units
- 4
- Prerequisite
- (MATH 2B or MATH 5B or AP Calculus BC with a minimum score of 4) and (MATH 3A and MATH 13) or (I&C SCI 6B and I&C SCI 6D)
Introduction to some of the mathematics used in the making and breaking of codes, with applications to classical ciphers and public key systems. Includes topics from number theory, probability, and abstract algebra.
MATH 173B Introduction to Cryptology II
- Units
- 4
- Prerequisite
- MATH 173A
Introduction to some of the mathematics used in the making and breaking of codes, with applications to classical ciphers and public key systems. The mathematics covered includes topics from number theory, probability, and abstract algebra.
MATH 175 Combinatorics
- Units
- 4
- Prerequisite
- (MATH 2B or MATH 5B or AP Calculus BC with a minimum score of 4) and MATH 13 with a minimum grade of C-
Introduction to combinatorics including basic counting principles, permutations, combinations, binomial coefficients, inclusion-exclusion, derangements, ordinary and exponential generating functions, recurrence relations, Catalan numbers, Stirling numbers, and partition numbers.
MATH 176 Mathematics of Finance
- Units
- 4
- Prerequisite
- MATH 3A
After reviewing tools from probability, statistics, and elementary differential and partial differential equations, concepts such as hedging, arbitrage, Puts, Calls, the design of portfolios, the derivation and solution of the Blac-Scholes, and other equations are discussed.
MATH 178 Mathematical Machine Learning
- Units
- 6
- Prerequisite
- MATH 10 and MATH 121A and MATH 130A
Theoretical introduction to Mathematical Machine Learning. Mathematical foundations and coding implementations using Python libraries such as scikit-learn and Keras. Supervised and unsupervised learning; regression and classification; loss functions; overfitting and the bias-complexity tradeoff. Prominent algorithms in machine learning.
MATH 180A Number Theory I
- Units
- 4
- Prerequisite
- MATH 3A and MATH 13 with a minimum grade of C-
Introduction to number theory and applications. Divisibility, prime numbers, factorization. Arithmetic functions. Congruences. Quadratic residue. Diophantine equations. Introduction to cryptography.
MATH 180B Number Theory II
- Units
- 4
- Prerequisite
- MATH 180A
Introduction to number theory and applications. Analytic number theory, character sums, finite fields, discrete logarithm, computational complexity. Introduction to coding theory. Other topics as time permits.
MATH 184 Topics in the History of Mathematics
- Units
- 4
- Prerequisite
- MATH 120A and MATH 140A
- Corequisite
- MATH 184L
Topics include mathematics in ancient times; the development of modern analysis; the evolution of geometric ideas. Students are assigned individual topics for term papers.
MATH 184L History of Mathematics Lesson Lab
- Units
- 1
- Prerequisite
- PHY SCI 5
- Corequisite
- MATH 184
Aspiring math teachers research, design, present, and peer review middle school or high school math lessons that draw from history of mathematics topics.
MATH 192 Studies in the Learning and Teaching of Secondary Mathematics
- Units
- 2
Focus is on historic and current mathematical concepts related to student learning and effective math pedagogy, with fieldwork in grades 6-14.
MATH 194 Problem Solving Seminar
- Units
- 2
Develops ability in analytical thinking and problem solving, using problems of the type found in the Mathematics Olympiad and the Putnam Mathematical Competition. Students taking the course in fall will prepare for and take the Putnam examination in December.
MATH 195W Mathematical Writing
- Units
- 4
- Prerequisite
- MATH 120A with a minimum grade of C- or MATH 121A with a minimum grade of C- or MATH 140A with a minimum grade of C-. Satisfactory completion of the Lower-Division Writing requirement
Techniques of mathematical writing and communication. Covers effectively writing mathematical papers, creating effective presentations, and communicating mathematics in a variety of media. Focuses on utilizing LaTeX for typesetting mathematics.
MATH 199A Special Studies in Mathematics
- Units
- 1-4
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
MATH 199B Special Studies in Mathematics
- Units
- 1-4
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
MATH 199C Special Studies in Mathematics
- Units
- 1-4
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
MATH 205A Introduction to Graduate Analysis
- Units
- 5
- Prerequisite
- Recommended: MATH 2E and MATH 3A and MATH 13, or equivalent
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
MATH 205B Introduction to Graduate Analysis
- Units
- 5
- Prerequisite
- MATH 205A with a minimum grade of B-
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
MATH 205C Introduction to Graduate Analysis
- Units
- 5
- Prerequisite
- MATH 205B with a minimum grade of B-
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
MATH 210A Real Analysis
- Units
- 4
- Prerequisite
- Recommended: MATH 140C or equivalent
Measure theory, Lebesgue integral, signed measures, Radon-Nikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the Riesz-Markov theorem, measure and outer measure, product measure spaces.
MATH 210B Real Analysis
- Units
- 4
- Prerequisite
- MATH 210A with a minimum grade of B-
Measure theory, Lebesgue integral, signed measures, Radon-Nikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the Riesz-Markov theorem, measure and outer measure, product measure spaces.
MATH 210C Real Analysis
- Units
- 4
- Prerequisite
- MATH 210B with a minimum grade of B-
Measure theory, Lebesgue integral, signed measures, Radon-Nikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the Riesz-Markov theorem, measure and outer measure, product measure spaces.
MATH 218A Introduction to Manifolds and Geometry
- Units
- 4
- Prerequisite
- Recommended: MATH 140C and MATH 121B, or equivalent
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
MATH 218B Introduction to Manifolds and Geometry
- Units
- 4
- Prerequisite
- MATH 218A with a minimum grade of B-
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
MATH 218C Introduction to Manifolds and Geometry
- Units
- 4
- Prerequisite
- MATH 218B with a minimum grade of B-
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
MATH 220A Analytic Function Theory
- Units
- 4
- Prerequisite
- Recommended: MATH 140C or equivalent
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
MATH 220B Analytic Function Theory
- Units
- 4
- Prerequisite
- MATH 220A with a minimum grade of B-
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
MATH 220C Analytic Function Theory
- Units
- 4
- Prerequisite
- MATH 220B with a minimum grade of B-
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
MATH 222A Topics in Several Complex Variables and Complex Geometry
- Units
- 4
- Prerequisite
- MATH 220C with a minimum grade of B-
Several Complex variables, d-bar problems, mappings, Kaehler geometry, de Rham and Dolbeault Theorems, Chern Classes, Hodge Theorems, Calabi conjecture, Kahler-Einstein geometry, Monge-Ampere.
MATH 222C Topics in Several Complex Variables and Complex Geometry
- Units
- 4
- Prerequisite
- MATH 222B with a minimum grade of B-
Several Complex variables, d-bar problems, mappings, Kaehler geometry, Le Rham and Dolbeault Theorems, Chern Classes, Hodge Theorems, Calabi conjecture, Kahler-Einstein geometry, Monge-Ampere.
MATH 225A Introduction to Numerical Analysis and Scientific Computing
- Units
- 4
- Prerequisite
- Recommended: MATH 3D and MATH 105B and MATH 140A and MATH 121A and MATH 112A, or equivalent
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Error analysis, approximation of functions, nonlinear equations.
MATH 225B Introduction to Numerical Analysis and Scientific Computing
- Units
- 4
- Prerequisite
- MATH 225A with a minimum grade of B-
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Numerical linear algebra, numerical solutions of differential equations; stability.
MATH 225C Introduction to Numerical Analysis and Scientific Computing
- Units
- 4
- Prerequisite
- Recommended: MATH 3D and MATH 105B and MATH 140A and MATH 121A and MATH 112A, or equivalent
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Numerical linear algebra, numerical solutions of differential equations; stability.
MATH 226A Computational Differential Equations
- Units
- 4
- Prerequisite
- Recommended: MATH 3D and MATH 112A and (MATH 140B or MATH 105B), or equivalent
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and Petrov-Galerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226A-B-C, respectively.
MATH 226B Computational Differential Equations
- Units
- 4
- Prerequisite
- Recommended: MATH 3D and MATH 112A and (MATH 140B or MATH 105B), or equivalent
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and Petrov-Galerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226A-B-C, respectively.
MATH 226C Computational Differential Equations
- Units
- 4
- Prerequisite
- Recommended: MATH 3D and MATH 112A and (MATH 140B or MATH 105B), or equivalent
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and Petrov-Galerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226A-B-C, respectively.
MATH 227A Mathematical and Computational Biology
- Units
- 4
- Prerequisite
- Recommended: MATH 2A and MATH 2B and MATH 3A, or equivalent
Analytical and numerical methods for dynamical systems, temporal-spatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Analytical methods.
MATH 227B Mathematical and Computational Biology
- Units
- 4
- Prerequisite
- MATH 227A with a minimum grade of B-
Analytical and numerical methods for dynamical systems, temporal-spatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Numerical simulations.
MATH 227C Mathematical and Computational Biology
- Units
- 4
- Prerequisite
- MATH 227A with a minimum grade of B-
Analytical and numerical methods for dynamical systems, temporal-spatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Probabilistic methods.
MATH 228 Topics in Applied Math Careers
- Units
- 2-4
- Prerequisite
- A basic course in programming; familiarity with probability and differential equations at the upper undergraduate level
Prepares students for math careers in industry.
MATH 230A Algebra
- Units
- 4
- Prerequisite
- Recommended: MATH 120A and MATH 121A and MATH 120B, or equivalent
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
MATH 230B Algebra
- Units
- 4
- Prerequisite
- MATH 230A with a minimum grade of B-
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
MATH 230C Algebra
- Units
- 4
- Prerequisite
- MATH 230B with a minimum grade of B-
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
MATH 232A Algebraic Number Theory
- Units
- 4
- Prerequisite
- MATH 230C with a minimum grade of B-
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, L-functions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
MATH 232B Algebraic Number Theory
- Units
- 4
- Prerequisite
- MATH 232A with a minimum grade of B-
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, L-functions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
MATH 232C Algebraic Number Theory
- Units
- 4
- Prerequisite
- MATH 232B with a minimum grade of B-
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, L-functions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
MATH 233A Algebraic Geometry
- Units
- 4
- Prerequisite
- MATH 230C with a minimum grade of B-
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, Riemann-Roch theorem, Jacobians, classification of curves and surfaces.
MATH 233B Algebraic Geometry
- Units
- 4
- Prerequisite
- MATH 233A with a minimum grade of B-
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, Riemann-Roch theorem, Jacobians, classification of curves and surfaces.
MATH 233C Algebraic Geometry
- Units
- 4
- Prerequisite
- MATH 233B with a minimum grade of B-
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, Riemann-Roch theorem, Jacobians, classification of curves and surfaces.
MATH 234B Topics in Algebra
- Units
- 4
- Prerequisite
- MATH 230C with a minimum grade of B-
Group theory, homological algebra, and other selected topics.
MATH 234C Topics in Algebra
- Units
- 4
- Prerequisite
- MATH 230C with a minimum grade of B-
Group theory, homological algebra, and other selected topics.
MATH 240A Differential Geometry
- Units
- 4
- Prerequisite
- MATH 218A with a minimum grade of B-
Riemannian manifolds, connections, curvature, and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
MATH 240B Differential Geometry
- Units
- 4
- Prerequisite
- MATH 240A with a minimum grade of B-
Riemannian manifolds, connections, curvature and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
MATH 240C Differential Geometry
- Units
- 4
- Prerequisite
- MATH 240B with a minimum grade of B-
Riemannian manifolds, connections, curvature and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
MATH 245A Topics in Geometric Analysis
- Units
- 4
- Prerequisite
- MATH 218A with a minimum grade of B-
Studies in selected areas of differential geometry, a continuation of MATH 240A-MATH 240B-MATH 240C. Topics addressed vary each quarter.
MATH 245B Topics in Geometric Analysis
- Units
- 4
- Prerequisite
- MATH 245A with a minimum grade of B-
Studies in selected areas of differential geometry, a continuation of MATH 240A-MATH 240B-MATH 240C. Topics addressed vary each quarter.
MATH 245C Topics in Geometric Analysis
- Units
- 4
- Prerequisite
- MATH 245B with a minimum grade of B-
Studies in selected areas of differential geometry, a continuation of MATH 240A-MATH 240B-MATH 240C. Topics addressed vary each quarter.
MATH 249 Topics in Differential Geometry
- Units
- 4
Studies in selected areas of differential geometry. Topics addressed vary each quarter.
MATH 250A Algebraic Topology
- Units
- 4
- Prerequisite
- Recommended: MATH 120B and MATH 141, or equivalent
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
MATH 250B Algebraic Topology
- Units
- 4
- Prerequisite
- MATH 250A with a minimum grade of B-
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
MATH 250C Algebraic Topology
- Units
- 4
- Prerequisite
- MATH 250B with a minimum grade of B-
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
MATH 260A Functional Analysis
- Units
- 4
- Prerequisite
- MATH 210C with a minimum grade of B- and MATH 220C with a minimum grade of B-
Normed linear spaces, Hilbert spaces, Banach spaces, Stone-Weierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the Gelfand-Neumark Theorem for commutative C*-algebras, the spectral theorem for bounded self-adjoint operators, unbounded operators on Hilbert spaces.
MATH 260B Functional Analysis
- Units
- 4
- Prerequisite
- MATH 260A with a minimum grade of B-
Normed linear spaces, Hilbert spaces, Banach spaces, Stone-Weierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the Gelfand-Neumark Theorem for commutative C*-algebras, the spectral theorem for bounded self-adjoint operators, unbounded operators on Hilbert spaces.
MATH 260C Functional Analysis
- Units
- 4
- Prerequisite
- MATH 260B with a minimum grade of B-
Normed linear spaces, Hilbert spaces, Banach spaces, Stone-Weierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the Gelfand-Neumark Theorem for commutative C*-algebras, the spectral theorem for bounded self-adjoint operators, unbounded operators on Hilbert spaces.
MATH 268C Topics in Functional Analysis
- Units
- 4
- Prerequisite
- MATH 268B
Selected topics such as spectral theory, abstract harmonic analysis, Banach algebras, operator algebras, and other related topics.
MATH 270A Probability
- Units
- 4
- Prerequisite
- MATH 210C with a minimum grade of B-. Recommended: MATH 130C or equivalent
Probability spaces, distribution, and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
MATH 270B Probability
- Units
- 4
- Prerequisite
- MATH 270A with a minimum grade of B-
Probability spaces, distribution and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
MATH 270C Probability
- Units
- 4
- Prerequisite
- MATH 270B with a minimum grade of B-
Probability spaces, distribution and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
MATH 271A Stochastic Processes
- Units
- 4
- Prerequisite
- MATH 210C with a minimum grade of B-
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes.
MATH 271B Stochastic Processes
- Units
- 4
- Prerequisite
- MATH 271A with a minimum grade of B-
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes.
MATH 271C Stochastic Processes
- Units
- 4
- Prerequisite
- MATH 271B with a minimum grade of B-
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes
MATH 274 Topics in Probability
- Units
- 4
- Prerequisite
- Recommended: MATH 270C
Selected topics, such as theory of stochastic processes, martingale theory, stochastic integrals, stochastic differential equations.
MATH 280A Mathematical Logic
- Units
- 4
- Prerequisite
- Recommended: MATH 150
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
MATH 280B Mathematical Logic
- Units
- 4
- Prerequisite
- MATH 280A with a minimum grade of B-
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
MATH 280C Mathematical Logic
- Units
- 4
- Prerequisite
- MATH 280B with a minimum grade of B-
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
MATH 281A Set Theory
- Units
- 4
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
MATH 281B Set Theory
- Units
- 4
- Prerequisite
- MATH 281A with a minimum grade of B-
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
MATH 281C Set Theory
- Units
- 4
- Prerequisite
- MATH 281B with a minimum grade of B-
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
MATH 282A Model Theory
- Units
- 4
Languages, structures, compactness, and completeness. Model-theoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. O-minimality. Applications to algebra.
MATH 282B Model Theory
- Units
- 4
- Prerequisite
- MATH 282A with a minimum grade of B-
Languages, structures, compactness and completeness. Model-theoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. O-minimality. Applications to algebra.
MATH 282C Model Theory
- Units
- 4
- Prerequisite
- MATH 282B with a minimum grade of B-
Languages, structures, compactness and completeness. Model-theoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. O-minimality. Applications to algebra.
MATH 290A Methods in Applied Mathematics
- Units
- 4
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, Euler-Lagrange equation. Second variation and Legendre condition.
MATH 290B Methods in Applied Mathematics
- Units
- 4
- Prerequisite
- MATH 290A
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, Euler-Lagrange equation. Second variation and Legendre condition.
MATH 290C Methods in Applied Mathematics
- Units
- 4
- Prerequisite
- MATH 290B
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, Euler-Lagrange equation. Second variation and Legendre condition.
MATH 295A Partial Differential Equations
- Units
- 4
- Prerequisite
- MATH 210C with a minimum grade of B-. Recommended: MATH 112B and MATH 112C or equivalent
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
MATH 295B Partial Differential Equations
- Units
- 4
- Prerequisite
- MATH 295A with a minimum grade of B-
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
MATH 295C Partial Differential Equations
- Units
- 4
- Prerequisite
- MATH 295B with a minimum grade of B-
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
MATH 296 Topics in Partial Differential Equations
- Units
- 4
- Prerequisite
- MATH 295C with a minimum grade of B-
Studies in selected areas of partial differential equations, a continuation of MATH 295A-MATH 295B-MATH 295C. Topics addressed vary each quarter.
MATH 298A Seminar
- Units
- 2
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
MATH 298B Seminar
- Units
- 2
- Prerequisite
- MATH 298A with a minimum grade of B-
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
MATH 298C Seminar
- Units
- 2
- Prerequisite
- MATH 298B with a minimum grade of B-
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
MATH 299A Supervised Reading and Research
- Units
- 1-12
Supervised reading and research with Mathematics faculty.
MATH 299B Supervised Reading and Research
- Units
- 1-12
- Prerequisite
- MATH 299A with a minimum grade of B-
Supervised reading and research with Mathematics faculty.
MATH 299C Supervised Reading and Research
- Units
- 1-12
- Prerequisite
- MATH 299B with a minimum grade of B-
Supervised reading and research with Mathematics faculty.
MATH 399 University Teaching
- Units
- 1-4
Limited to Teaching Assistants.