Mathematics - undergraduate program

Mathematics

[ undergraduate program | graduate program | faculty ]

All courses, faculty listings, and curricular and degree requirements described herein are subject to change or deletion without notice.

Courses

For course descriptions not found in the UC San Diego General Catalog 2019–20, please contact the department for more information.

All prerequisites listed below may be replaced by an equivalent or higher-level course. The listings of quarters in which courses will be offered are only tentative. Please consult the Department of Mathematics to determine the actual course offerings each year.

Lower Division

MATH 2. Introduction to College Mathematics (4)

A highly adaptive course designed to build on students’ strengths while increasing overall mathematical understanding and skill. 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. Workload credit only—not for baccalaureate credit. Prerequisites: Math Placement Exam qualifying score.

MATH 3C. Precalculus (4)

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. Prerequisites: Math Placement Exam qualifying score.

MATH 4C. Precalculus for Science and Engineering (4)

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. (No credit given if taken after MATH 1A/10A or 2A/20A. Two units of credit given if taken after MATH 3C.) Prerequisites: Math Placement Exam qualifying score or MATH 3C with a grade of C– or better.

MATH 10A. Calculus I (4)

Differential calculus of functions of one variable, with applications. Functions, graphs, continuity, limits, derivatives, tangent lines, optimization problems. (No credit given if taken after or concurrent with MATH 20A.) Prerequisites: Math Placement Exam qualifying score, or AP Calculus AB score of 2, or SAT II Math Level 2 score of 600 or higher, or MATH 3C, or MATH 4C.

MATH 10B. Calculus II (4)

Integral calculus of functions of one variable, with applications. Antiderivatives, definite integrals, the Fundamental Theorem of Calculus, methods of integration, areas and volumes, separable differential equations. (No credit given if taken after or concurrent with MATH 20B.) Prerequisites: AP Calculus AB score of 3, 4, or 5 (or equivalent AB subscore on BC exam), or MATH 10A, or MATH 20A.

MATH 10C. Calculus III (4)

Introduction to functions of more than one variable. Vector geometry, partial derivatives, velocity and acceleration vectors, optimization problems. (No credit given if taken after or concurrent with 20C.) Prerequisites: AP Calculus BC score of 3, 4, or 5, or MATH 10B, or MATH 20B.

MATH 11. Calculus-Based Introductory Probability and Statistics (5)

Events and probabilities, conditional probability, Bayes’ formula. Discrete and continuous random variables: mean, variance; binomial, Poisson distributions, normal, uniform, exponential distributions, central limit theorem. Sample statistics, confidence intervals, hypothesis testing, regression. Applications. Introduction to software for probabilistic and statistical analysis. Emphasis on connections between probability and statistics, numerical results of real data, and techniques of data analysis. Prerequisites: AP Calculus BC score of 3, 4, or 5, or MATH 10B or MATH 20B.

MATH 15A. Introduction to Discrete Mathematics (4)

Basic discrete mathematical structure: sets, relations, functions, sequences, equivalence relations, partial orders, and number systems. Methods of reasoning and proofs: propositional logic, predicate logic, induction, recursion, and pigeonhole principle. Infinite sets and diagonalization. Basic counting techniques; permutation and combinations. Applications will be given to digital logic design, elementary number theory, design of programs, and proofs of program correctness. Students who have completed MATH 109 may not receive credit for MATH 15A. Credit not offered for both MATH 15A and CSE 20. Equivalent to CSE 20. Prerequisites: CSE 8B or CSE 11 with a grade of C– or better.

MATH 18. Linear Algebra (4)

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. Students may not receive credit for both MATH 18 and 31AH. Prerequisites: Math Placement Exam qualifying score, or AP Calculus AB score of 2, or SAT II Math Level 2 score of 600 or higher, or MATH 3C, or MATH 4C, or MATH 10A, or MATH 20A. Students who have not completed listed prerequisites may enroll with consent of instructor.

MATH 20A. Calculus for Science and Engineering (4)

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.) Prerequisites: Math Placement Exam qualifying score, or AP Calculus AB score of 3 (or equivalent AB subscore on BC exam), or SAT II MATH 2C score of 650 or higher, or MATH 4C or MATH 10A.

MATH 20B. Calculus for Science and Engineering (4)

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.) Prerequisites: AP Calculus AB score of 4 or 5, or AP Calculus BC score of 3, or MATH 20A with a grade of C– or better, or MATH 10B with a grade of C– or better, or MATH 10C with a grade of C– or better.

MATH 20C. Calculus and Analytic Geometry for Science and Engineering (4)

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.) Prerequisites: AP Calculus BC score of 4 or 5, or MATH 20B with a grade of C– or better.

MATH 20D. Introduction to Differential Equations (4)

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. Prerequisites: MATH 20C (or MATH 21C) or MATH 31BH with a grade of C– or better.

MATH 20E. Vector Calculus (4)

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. Prerequisites: MATH 18 or MATH 20F or MATH 31AH and MATH 20C (or MATH 21C) or MATH 31BH with a grade of C– or better.

MATH 31AH. Honors Linear Algebra (4)

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.) Prerequisites: AP Calculus BC score of 5 or consent of instructor.

MATH 31BH. Honors Multivariable Calculus (4)

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.) Prerequisites: MATH 31AH with a grade of B– or better, or consent of instructor.

MATH 31CH. Honors Vector Calculus (4)

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. Prerequisites: MATH 31BH with a grade of B– or better, or consent of instructor.

MATH 87. Freshman Seminar (1)

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 fifteen to twenty students, with preference given to entering freshman. Prerequisites: none.

MATH 95. Introduction to Teaching Math (2)

(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. Prerequisites: none.

MATH 96. Putnam Seminar (1)

Students will develop skills in analytical thinking as they solve and present solutions to challenging mathematical problems in preparation for the William Lowell Putnam Mathematics Competition, a national undergraduate mathematics examination held each year. Students must sit for at least one half of the Putnam exam (given the first Saturday in December) to receive a passing grade. P/NP grades only. May be taken for credit up to four times. Prerequisites: AP Calculus AB score of 4 or more, or AP Calculus BC score of 3 or more, or MATH 20A.

MATH 99R. Independent Study (1)

Independent study or research under direction of a member of the faculty. Prerequisites: Must be of first-year standing and a Regent’s Scholar.

Upper Division

MATH 100A. Abstract Algebra I (4)

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.) Prerequisites: MATH 31CH or MATH 109 or consent of instructor.

MATH 100B. Abstract Algebra II (4)

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.) Prerequisites: MATH 100A or consent of instructor.

MATH 100C. Abstract Algebra III (4)

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. Prerequisites: MATH 100B or consent of instructor.

MATH 102. Applied Linear Algebra (4)

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. Prerequisites: MATH 18 or MATH 20F or MATH 31AH and MATH 20C. Students who have not completed listed prerequisites may enroll with consent of instructor.

MATH 103A. Modern Algebra I (4)

First course in a two-quarter introduction to abstract algebra with some applications. Emphasis on group theory. Topics include definitions and basic properties of groups, properties of isomorphisms, subgroups. (Students may not receive credit for both MATH 100A and MATH 103A.) Prerequisites: MATH 31CH or MATH 109 or consent of instructor.

MATH 103B. Modern Algebra II (4)

Second course in a two-quarter introduction to abstract algebra with some applications. Emphasis on rings and fields. Topics include definitions and basic properties of rings, fields, and ideals, homomorphisms, irreducibility of polynomials. (Students may not receive credit for both MATH 100B and MATH 103B.) Prerequisites: MATH 103A or MATH 100A or consent of instructor.

MATH 104A. Number Theory I (4)

Elementary number theory with applications. Topics include unique factorization, irrational numbers, residue systems, congruences, primitive roots, reciprocity laws, quadratic forms, arithmetic functions, partitions, Diophantine equations, distribution of primes. Applications include fast Fourier transform, signal processing, codes, cryptography. Prerequisites: MATH 100B or MATH 103B. Students who have not completed the listed prerequisite(s) may enroll with consent of instructor.

MATH 104B. Number Theory II (4)

Topics in number theory such as finite fields, continued fractions, Diophantine equations, character sums, zeta and theta functions, prime number theorem, algebraic integers, quadratic and cyclotomic fields, prime ideal theory, class number, quadratic forms, units, Diophantine approximation, p-adic numbers, elliptic curves. Prerequisites: MATH 104A or consent of instructor.

MATH 104C. Number Theory III (4)

Topics in algebraic and analytic number theory, with an advanced treatment of material listed for MATH 104B. Prerequisites: Math 104B or consent of instructor.

MATH 105. Basic Number Theory (4)

The course will cover the basic arithmetic properties of the integers, with applications to Diophantine equations and elementary Diophantine approximation theory. No credit offered for MATH 105 if MATH 104A taken previously or concurrently. Prerequisites: MATH 31CH or MATH 109. Students who have not completed the listed prerequisites may enroll with consent of instructor.

MATH 106. Introduction to Algebraic Geometry (4)

Plane curves, Bezout’s theorem, singularities of plane curves. Affine and projective spaces, affine and projective varieties. Examples of all the above. Instructor may choose to include some commutative algebra or some computational examples. Prerequisites: MATH 100B or MATH 103B. Students who have not completed the listed prerequisites may enroll with consent of instructor.

MATH 109. Mathematical Reasoning (4)

This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations and epsilon-delta proofs. Required of all departmental majors. Prerequisites: MATH 18 or MATH 20F or MATH 31AH, and MATH 20C. Students who have not completed listed prerequisites may enroll with consent of instructor.

MATH 110. Introduction to Partial Differential Equations (4)

An introduction to partial differential equations focusing on equations in two variables. Topics include the heat and wave equation on an interval, Laplace’s equation on rectangular and circular domains, separation of variables, boundary conditions and eigenfunctions, introduction to Fourier series, software methods for solving equations. Formerly MATH 110A. (Students may not receive credit for MATH 110 and MATH 110A.) Prerequisites: MATH 18 or MATH 20F or MATH 31AH and MATH 20D and MATH 20E or MATH 31CH. Students who have not completed listed prerequisites may enroll with consent of instructor.

MATH 111A. Mathematical Modeling I (4)

An introduction to mathematical modeling in the physical and social sciences. Topics vary, but have included mathematical models for epidemics, chemical reactions, political organizations, magnets, economic mobility, and geographical distributions of species. May be taken for credit two times when topics change. Prerequisites: MATH 20D, MATH 18 or MATH 20F or MATH 31AH, and MATH 109 or MATH 31CH. Students who have not completed listed prerequisites may enroll with consent of instructor.

MATH 111B. Mathematical Modeling II (4)

Continued study on mathematical modeling in the physical and social sciences, using advanced techniques that will expand upon the topics selected and further the mathematical theory presented in MATH 111A. Prerequisites: MATH 111A or consent of instructor.

MATH 120A. Elements of Complex Analysis (4)

uction to Stochastic Processes...