MATH 105
The Mathematical Experience
An introduction to the scope, power, and spirit of mathematics. Topics, chosen to convey the character of mathematical inquiry, may vary; they include euclidean and non-euclidean geometry, number theory, topology, graph theory, infinity, paradoxes, set theory, and logic. Intended for students with limited preparation in mathematics. 6 units. Prerequisite: Sophomore standing
MATH 107
Elementary Statistics
For students in all disciplines. Provides the background needed to evaluate statistical arguments found in newspapers, magazines, reports, and journals and the logic and techniques necessary to perform responsible elementary statistical analysis. Students who have completed a calculus course should elect Mathematics 207 rather than Mathematics 107. 6 units. Prerequisite: Sophomore standing. Only one of MATH 107, 117, or 207 may be taken for credit.
MATH 117
Elementary Statistics
For students in all disciplines. Provides background needed to evaluate statistical arguments found in newspapers, magazines, reports, and journals and the logic and techniques necessary to perform responsible elementary statistical analysis, including computer-aided data analysis. Winter Term laboratory component emphasizes analysis of social science data sets, and Spring Term laboratory component emphasizes analysis of natural science data sets. Students who have completed a calculus course should elect Mathematics 207 rather than Mathematics 107 or 117. 6 units. Prerequisite: Sophomore standing. Only one of MATH 107, 117, or 207 may be taken for credit.
MATH 120
Applied Calculus I
An introduction to calculus that stresses applications to the life and social sciences. Topics include derivatives, integrals, optimization, and exponential and logarithmic functions. Mathematics 120 and 130 do not prepare students for more advanced courses. 6 units. Prerequisite: Three years of high school mathematics; MATH 120 and 140 cannot both be taken for credit.
MATH 130
Applied Calculus II
Differential and integral calculus in several variables, including optimization, partial derivatives, and multiple integrals. Also applications of integration and an introduction to differential equations. Stresses applications to the life and social sciences. 6 units. Prerequisite: MATH 120
MATH 140
Calculus I
Functions, limits, derivatives, the Mean Value Theorem, definition and properties of integrals, the Fundamental Theorem of Calculus, and applications to related rates, curve sketching, and optimization problems. Placement exam not required. 6 units. Prerequisite: Four years of high school mathematics; MATH 120 and 140 cannot both be taken for credit.
MATH 150
Calculus II
Applications of integration, exponential and logarithmic functions, techniques of integration, infinite sequences and series, and Taylor series. 6 units. Prerequisite: Advanced placement, MATH 140, or MATH 120 and consent of instructor.
MATH 160
Calculus III
Functions of two or more variables, partial derivatives, chain rules, optimization, vectors, derivatives of vector-valued functions, Lagrange multipliers, multiple integrals, line integrals, and Green’s Theorem. 6 units. Prerequisite: MATH 150 or advanced placement
MATH 207
Introduction to Probability and Statistics
A survey of statistical methods including their mathematical foundation and their implementations on a computer. Topics include descriptive statistics and graphs, simple linear regression, random variables and their distributions, conditional probability, independence, sampling distributions, the Central Limit Theorem, and parametric and nonparametric tests of hypotheses. Laboratory component emphasizes analysis of economic data sets. 6 units. Prerequisite: MATH 120 or 140; Only one of MATH 207, 107, or 117 may be taken for credit.
MATH 210
Differential Equations with Linear Algebra
A study of differential equations and related techniques in linear algebra. Topics include first-order equations and their applications, existence and uniqueness of solutions, second-order linear equations and their applications, series solutions, systems of first-order equations, vector spaces and dimension, linear transformations, and eigenvalues. 6 units. Prerequisite: MATH 160, or MATH 150 and consent of instructor
MATH 220
Applied Combinatorics
An introduction to logic, proofs by mathematical induction, and elementary combinatorics. Additional topics include recurrence relations, generating functions, and the principle of inclusion-exclusion. 6 units. Prerequisite: MATH 150
MATH 300
Foundations of Algebra
An introduction to the rigorous study of mathematics. Topics include elementary theory of sets and mappings, number theory, equivalence relations, finite groups, homomorphisms, quotient groups, and rings. 6 units. Prerequisite: MATH 207, 210, or 220
MATH 310
Foundations of Analysis
A study of the concepts that underlie mathematical analysis: the completeness of the real numbers, convergence, continuity, derivatives, integrals, infinite series, and, if time permits, an introduction to metric spaces or Fourier series. 6 units. Prerequisite: MATH 300
MATH 410
Linear Algebra
The study of finite and infinite dimensional vector spaces, and linear transformations between such spaces. Starting with n-dimensional Euclidean space, the focus will move toward greater abstraction. Topics include dimension, the fundamental spaces of linear transformations, spectral theory, and applications. Other topics could include normed, inner product, and function spaces. 6 units. Prerequisite: MATH 300
MATH 420
Numerical Analysis
Computer approximated (numerical) solutions to a variety of problems with an emphasis on error analysis. Interpolation, evaluation of polynomials and series, solution of linear and non-linear equations, eigenvectors, quadrature (integration), and differential equations. 6 units. Prerequisite: MATH 300 and CMSC 110 or CMSC 150
MATH 435
Optimization
The study of local and global maximums and minimums of function, given various sorts of constraints. Linear problems and the simplex algorithm, general non-linear problems and the Kuhn-Tucker conditions, convex problems. Perturbation of problem parameters and duality. Applications to a wide variety of fields, including economics, game theory, and operations research. 6 units. Prerequisite: MATH 310
MATH 440
Probability Theory
The mathematics of chance: probability, discrete and continuous random variables and their distributions, moments, jointly distributed random variables, conditional distributions, the Central Limit Theorem, and weak and strong convergence. 6 units. Prerequisite: MATH 310
MATH 445
Mathematical Statistics
The theory of probability applied to problems in statistics. Topics include sampling theory, point and interval estimation, tests of statistical hypotheses, regression, and analysis of variance. Computer lab component is used to analyze real-world case studies. 6 units. Prerequisite: MATH 310 and MATH 440
MATH 495
Teaching Seminar
A seminar on teaching mathematics intended for students seeking secondary certification. Practice with and advice on lecture, small group, and one-on-one situations. Outside readings on the philosophy and techniques of teaching mathematics, professional standards, curriculum issues, and resources. 2 units.
MATH 515
Theory of Computation
A study of programming in the abstract, leading to an understanding of the precise nature and limitations of computing machines. Topics include universal computing machines such as Turing machines, decidable and undecidable predicates, regular and pushdown automata, and regular and context-free grammars. 6 units. Also listed as Computer Science 515. Prerequisite: MATH 300 and CMSC 150
MATH 525
Graph Theory
A survey of graph theory that balances the abstract theory of graphs with a wide variety of algorithms and applications to “real world” problems. Topics include trees, Euler tours and Hamilton cycles, matchings, colorings, directed graphs, and networks. 6 units. Prerequisite: MATH 300
MATH 530
Topics in Geometry
The axiomatic development of euclidean and non-euclidean geometry, including the historical and philosophical issues raised by the “non-euclidean revolution.” Additional topics, such as projective or differential geometry and convexity, may be included. 6 units. Prerequisite: MATH 300
MATH 535
Complex Analysis
An introduction to functions of a complex variable, the Cauchy-Riemann equations, conformal mappings, Cauchy’s theorem, Cauchy’s integral formula, Taylor and Laurent series, and a sampling, as time and interest permit, of the corollaries to Cauchy’s theorem. 6 units. Prerequisite: MATH 310
MATH 540
Mathematical Logic
Establishes the basic syntactical tools needed to develop the semantics of first-order logic with equality, including the completeness and compactness theorems. Formal number theory and the theory of recursive functions are developed, culminating in the proof of Gödel’s Incompleteness Theorem. 6 units. Prerequisite: MATH 300
MATH 545
Rings and Fields
Modern algebra with topics selected from group theory, ring theory, field theory, classical geometric construction problems, and Galois theory. Emphasis on the use of mathematical abstraction to illuminate underlying relationships and structure. 6 units. Prerequisite: MATH 300
MATH 546
Groups and Symmetry
The study of symmetry and symmetric transformations as they relate to the geometric and topological structure of various spaces. 6 units. Prerequisite: MATH 300
MATH 550
Topics in Analysis
Selected topics in analysis, generally chosen from multivariate analysis, Lebesgue measure and integration, Fourier analysis, calculus on manifolds, the qualitative properties of analytical models. 6 units. Prerequisite: MATH 310
MATH 560
Topology
A study of metric and topological spaces, including continuity, compactness, connectedness, product and quotient spaces. Additional topics may include Zorn’s Lemma, separation properties, surfaces, the fundamental group, and fixed point theorems. 6 units. Prerequisite: MATH 310
MATH 600
History of Mathematics
A study of the history of mathematics from the ancient Greeks through the present, emphasizing the role of mathematics in scientific advances, the work of great mathematicians, and the modern branching of the subject into a multitude of specialties. 6 units. Prerequisite: MATH 310
MATH 190, 390, 590, 690
Tutorial Studies in Mathematics
Advanced work in mathematics on topics not covered in regular offerings. Variable units. Prerequisite: Counter registration required
MATH 199, 399, 599, 699
Independent Study in Mathematics
Guided independent study of an advanced topic in undergraduate mathematics or supervised work on an undergraduate research project, generally culminating in a final presentation and/or paper. Variable units. Prerequisite: Counter registration required