# Course Descriptions

Mathematics

For students majoring in arts and humanities. Topics chosen from set theory, logic, counting techniques, number systems, graph theory, financial management, voting methods, and other suitable areas. Material will generally be presented in a setting that allows students to participate in the discovery and development of important mathematical ideas. Emphasis on problem solving and doing mathematics.

Introduction to finite mathematics with applications to the social sciences. Sets and set operations, Venn diagrams, trees, permutations, combinations, probability (including conditional probability and Bernoulli processes), discrete random variables, probability distributions, and expected value.

Introduction to differential and integral calculus with applications to the social sciences. Ordinarily, only one of MATH 7, 11, or 30 may be taken for credit.

Elementary topics in statistics, including descriptive statistics, regression, probability, random variables and distributions, the central limit theorem, confidence intervals and hypothesis testing for one population and for two populations, goodness of fit, and contingency tables.

College algebra and trigonometry for students intending to take calculus. Does not fulfill the University Core Curriculum requirement in mathematics.

Optional lab component for Math 9

Limits and differentiation. Methods and applications of differentiation. Ordinarily, only one of MATH 11 or 30 may be taken for credit. Note: MATH 11 is not a suitable prerequisite for MATH 31 without additional preparation. Prerequisite: High school trigonometry and either Calculus Readiness Exam or MATH 9. If MATH 9 is taken, a grade of C- or higher is strongly recommended before taking MATH 11.

Optional lab component for Math 11

Differentiation and applications, introduction to integration. Ordinarily, only one of MATH 7, 11, or 30 may be taken for credit. Prerequisite: Four years of high school mathematics (including trigonometry) or satisfactory grade in MATH 9. If MATH 9 is taken, a grade of C- or higher is strongly recommended before taking MATH 11.

Further applications of differentiation. Integration and the fundamental theorem of calculus. Methods and applications of integration. Only one of MATH 12 or 31 may be taken for credit. Note: MATH 30 is not a suitable prerequisite for MATH 12 without additional preparation. Prerequisite: MATH 11 or equivalent. A grade of C or higher in MATH 11 is strongly recommended before taking MATH 12.

Further applications of differentiation. Integration and the fundamental theorem of calculus. Methods and applications of integration. Only one of MATH 12H or 31 may be taken for credit. Note: MATH 30 is not a suitable prerequisite for MATH 12 without additional preparation. Prerequisite: MATH 11 or equivalent. A grade of C- or higher in MATH 11 is strongly recommended before taking MATH 12H.

Taylor series, vectors, quadric surfaces, and partial derivatives, including optimization of functions with multiple variables. Prerequisite: MATH 12 or equivalent. A grade of C- or higher in MATH 12 is strongly recommended before taking MATH 13.

Vector functions, line integrals, multiple integrals, flux, divergence theorem, and Green's theorem. Prerequisite: MATH 13 or equivalent. A grade of C- or higher in MATH 13 is strongly recommended before taking MATH 14.

Explicit solution techniques for first order differential equations and higher order linear differential equations. Use of numerical and Laplace transform methods. Applications. Only one of MATH 22, 23 or AMTH 106 may be taken for credit. Mathematics majors should take MATH 23, which will substitute for MATH 22. Prerequisite: MATH 13.

Sequences, series, and analytic functions. Use of explicit, numerical, and series methods to solve ordinary differential equations. Complex numbers. Only one of MATH 22, MATH 23, or AMTH 106 may be taken for credit. Prerequisite: MATH 13

Differentiation and its applications to business, including marginal cost and profit, maximization of revenue, profit, utility, and cost minimization. Natural logarithms and exponential functions and their applications, including compound interest and elasticity of demand. Study of the theory of the derivative normally included in MATH 11, except trigonometric functions not included here. Ordinarily, only one of MATH 11 or 30 may be taken for credit. Note: MATH 30 is not a suitable prerequisite for MATH 12 without additional preparation. Prerequisite: Calculus Readiness Exam or MATH 9. If MATH 9 is taken, a grade of C- or higher is strongly recommended before taking MATH 30.

Optional lab component for Math 30

Integration and its applications to business, including consumer surplus and present value of future income. Functions of several variables and their derivatives. Emphasis throughout the sequence on mathematical modeling, the formulation of practical problems in mathematical terms. Only one of MATH 12 or 31 may be taken for credit. Note: MATH 11 is not a suitable prerequisite for MATH 31 without additional preparation. Prerequisite: MATH 30 or equivalent. A grade of C- or higher in MATH 30 is strongly recommended before taking MATH 31.

Problem solving and logical thinking approach to whole numbers: their nature, counting, place value, computational operations, properties, and patterns. Intuitive two-dimensional geometry and measurement, especially metric. Note: This course requires participation in community-based learning experiences off campus.

Problem solving and logical thinking approach to fractional numbers, integers, rational numbers and real numbers: their nature, computational operations, properties, and patterns, intuitive three-dimensional geometry and measurement, especially metric. Functions, relations, and graphs. Prerequisite: MATH 44.

Predicate logic, methods of proof, sets, functions, sequences, modular arithmetic, cardinality, induction, elementary combinatorial analysis, recursion, and relations. Also listed as COEN 19.

Groups, homomorphisms, isomorphisms, quotient groups, fields, integral domains; applications to number theory. Prerequisite: MATH 51 or permission of the instructor.

Vector spaces, linear transformations, algebra of matrices, eigenvalues and eigenvectors, and inner products. Prerequisite: MATH 13.

Basic techniques of problem solving. Topics in algebra, geometry, and analysis. (4 units)

An introduction to writing and research in mathematics. Techniques in formulating research problems, standard proof methods, and proof writing. Practice in mathematical exposition for a variety of audiences. Strongly recommended for mathematics and computer science majors beginning their upper-division course work. MATH 100 may not be taken to fulfill any mathematics or computer science upper-division requirements for students majoring or minoring in mathematics or computer science.

Topics from advanced Euclidean, projective, and non-Euclidean geometries. Symmetry. Offered in alternate years.

Vector calculus, functions of several variables, line integrals, Stokes' theorem, and the divergence theorem. Prerequisites: MATH 14, 51, and 53.

Abstract vector spaces, dimensionality, linear transformations, isomorphisms, matrix algebra, Eigenspaces and diagonalization, Cayley-Hamilton Theorem, canonical forms, unitary and Hermitian operators, applications. Prerequisite: MATH 53

Analytic functions. Cauchy integral theorems, power series, conformal mapping. Riemann surfaces. Offered in alternate years.

Topics from the theory of groups. Offered in alternate years. Prerequisites: MATH 52 and 53.

Rings and ideals, algebraic extensions of fields, and the Galois theory. Offered in alternate years. Prerequisite: MATH 111.

Topological spaces and continuous functions. Separability and compactness. Introduction to covering spaces or combinatorial topology. Offered in alternate years. Prerequisite: MATH 14 and 51 (102 recommended).

Sample spaces; conditional probability; independence; random variables; discrete and continuous probability distributions; expectation; moment-generating functions; weak law of large numbers; central limit theorem. Prerequisite: MATH 14. (5 units)

Confidence intervals and hypothesis testing. Maximum likelihood estimation. Analysis of variance (ANOVA) and analysis of categorical data. Simple and multiple linear regression. Optional topics may include sufficiency, the Rao-Blackwell theorem, logistic regression, and nonparametric statistics. Applications. Prerequisites: MATH 53 or permission of instructor and MATH 122.

Introduction to Ito calculus and stochastic differential equations. Discrete lattice models. Models for the movement of stock and bond prices using Brownian motion and Poisson processes. Pricing models for equity and bond options via Black-Scholes and its variants. Optimal portfolio allocation. Solution techniques will include Monte Carlo and finite difference methods. Prerequisite: MATH 53 or permission of instructor and MATH 122 or AMTH 108. Cross listed with FNCE 116 and 3490 and AMTH 367.

Deductive theories. Theories and models. Consistency, completeness, decidability. Theory of models. Cardinality of models. Some related topics of metamathematics and foundations. Open to upper-division science and mathematics students and to philosophy majors having sufficient logical background. Offered on demand.

Naive set theory. Cardinal and ordinal arithmetic. Axiom of choice and continuum hypothesis. Axiomatic set theory. Offered on demand.

Linear partial differential equations with applications in physics and engineering, including wave (hyperbolic), heat (parabolic), and Laplace (elliptic) equations. Solutions on bounded and unbounded domains using Fourier series and Fourier transforms. Introduction to nonlinear partial differential equations. Offered in alternate years. Prerequisite: MATH 14. Recommended: MATH 22 or 23 or AMTH 106.

Rigorous investigation of the real number system. Concepts of limit, continuity, differentiability of functions of one real variable, uniform convergence, and theorems of differential and integral calculus. Offered in alternate years. Prerequisite: MATH 51 and either 102 or 105.

Continuation of MATH 153. Offered in alternate years. Prerequisite: MATH 153.

Solutions to systems of linear differential equations. Behavior of nonlinear autonomous two-dimensional systems. Uniqueness and existence of solutions. Offered in alternate years. Prerequisites: MATH 53 or permission of instructor.

Algebraic background. Transportation problem. General simplex methods. Linear programming and theory of games. Numerical methods. Offered in alternate years. Also listed as CSCI 165.

Numerical algorithms and techniques for solving mathematical problems. Linear systems, integration, approximation of functions, solution of nonlinear equations. Analysis of errors involved in the various methods. Direct methods and iterative methods. Also listed as CSCI 166. Prerequisites: CSCI 10 or equivalent, and MATH 53, or permission of the instructor.

A selection of mathematical concepts with their historical context. Offered in alternate years. Prerequisite: Upper-division standing in a science major.

Use of induction, analogy, and other techniques in solving mathematical problems. Offered in alternate years.

Introduction to curves and surfaces. Frenet-Serret formulas, Gauss' Theorema Egregium, Gauss-Bonnet theorem. Offered in alternate years. Prerequisite: MATH 53.

Fundamental theorems on divisibility, primes, congruences. Number theoretic functions. Diophantine equations. Quadratic residues. Partitions. Offered in alternate years. Prerequisite: MATH 52.

Permutations and combinations, generating functions, recursion relations, inclusion-exclusion, Pólya counting theorem, and a selection of topics from combinatorial geometry, graph enumeration, and algebraic combinatorics. Prerequisite: MATH 51

Selected topics from planarity, connectedness, trees (enumeration), digraphs, graph algorithms, and networks. Offered in alternate years. Prerequisite: MATH 51.

History, classical cryptosystems, stream ciphers, AES, RSA, discrete log over finite fields and elliptic curves, stream ciphers, and signatures. Offered in alternate years. This course followed by CSCI 181.

Advanced topics in algebra, geometry, or analysis. Research projects. May be repeated for credit.

Research project supervised by a faculty member in the department. Permission of the professor directing the research must be secured before registering for this course.

Offered each year in an advanced area of mathematics not ordinarily covered in the regularly offered courses. Often an area of current interest. May be repeated for credit.

Guided study related to off-campus practical work experience in mathematics or statistics. Enrollment restricted to majors or minors of the department. Prerequisite: Approval of a faculty sponsor.

Reading and investigation for superior students under the direction of a staff member. This can be used only to extend, not to duplicate, the content of other courses. May be repeated for credit.

Computer Science

An overview course providing multiple perspectives on computing. Students will learn the structures of computer programming without writing code, gain high-level understanding of important computing systems such as the Internet and databases, and discuss the impact of technology on society. Offered on demand.

Introduction to computer programming and computer science. Basic programming structures, conditionals, loops, functions, arrays. Topics relating to the applications of and social impact of computing, including privacy, artificial intelligence, computation in physics, psychology, and biology. Discussion of cryptography, computation through history, networks, hardware. Includes weekly lab. CSCI 10 may not be taken for credit if the student has received credit for COEN 10 or a similar introductory programming course.

Object-oriented programming techniques using C++: abstract data types and objects; encapsulation; inheritance; polymorphism; the Standard Template Library; the five phases of software development (specification, design, implementation, analysis, and testing). Includes weekly lab. Prerequisite: A grade of C- or better in CSCI 10 or equivalent.

Specification, implementations, and analysis of basic data structures (stacks, queues, graphs, hash tables, binary trees) and their applications in sorting and searching algorithms. Prerequisite: A grade of C- or better in CSCI 60 or equivalent. CSCI 61 and COEN 12 cannot both be taken for credit.

Basic techniques of problem solving. Topics in computer science.

Classification of automata, formal languages, and grammars. Chomsky hierarchy. Representation of automata and grammars, BNF. Deterministic and nondeterministic finite state automata. Regular expressions and languages. Push-down automata. Context-free languages. Context-sensitive grammars and linear bounded automata. Recursively enumerable languages. Turing machines; normal forms; undecidability. Prerequisites: MATH 51 or equivalent.

Time and space-bounded complexity classes. Reducibility and completeness. The polynomial hierarchy. Nonuniform complexity classes. Probabilistic complexity classes. Offered in alternate years. Prerequisite: CSCI 161.

Introduction to techniques of design and analysis of algorithms: asymptotic notations and running times of recursive algorithms. Design strategies: brute-force, divide and conquer, decrease and conquer, transform and conquer, dynamic programming, greedy technique. Intractability: P and NP, approximation algorithms. Also listed as COEN 179. Prerequisites: MATH 51 and CSCI 61, or equivalents.

Advanced techniques for the design, analysis and implementation of algorithms with an emphasis on graph algorithms and application: routing and shortest paths, network flow, vertex coloring, social network analysis and geometric/topological graph algorithms. Offered in alternate years. Prerequisite: CSCI 163A or COEN 179.

Techniques for generation of probability distributions. Monte Carlo methods for physical systems. Applications of computer models, for example, queuing, scheduling, simulation of physical or human systems. Offered in alternate years. Prerequisite: CSCI 10 or equivalent (MATH 122 recommended).

Algebraic background. Transportation problem. General simplex methods. Linear programming and theory of games. Numerical methods. Offered in alternate years. Also listed as MATH 165.

Numerical algorithms and techniques for solving mathematical problems. Linear systems, integration, approximation of functions, solution of nonlinear equations. Analysis of errors involved in the various methods. Direct methods and iterative methods. Also listed as MATH 166. Prerequisites: CSCI 10 or equivalent, and MATH 53, or permission of the instructor.

Switching algebra and Boolean algebra. Minimization via Karnaugh maps and Quine-McCluskey, state compatibility, and equivalence. Machine minimization. Faults. State identification, finite memory, definiteness, information losslessness. Offered in alternate years.

Systematic and comprehensive overview of interactive computer graphics, such as mathematical techniques for picture transformations and curve and surface approximations. Offered in alternate years. Prerequisites: CSCI 10 or equivalent, and Math 13.

Comparative study of major classes of programming languages, with particular focus on functional programming. Introduction to theoretical definitions of languages and run-time concerns, with emphasis on strong points and weak points of various languages and on using the appropriate language for a given task. Programs written in several languages (e.g., Python, Java, Scala). Offered in alternate years. Prerequisites: CSCI 61 and MATH 51, or permission of the instructor.

Key management, hash functions, stream ciphers, web of trust, time stamping, secret sharing, quantum cryptography, running time analysis, cryptanalytic techniques. Offered in alternative years. Prerequisites: MATH 178 and CSCI 10 or equivalent.

History and applications; Techniques: substitution, transform domain, distortion, statistical, cover; Evaluation: benchmarking, statistical analysis; Attacks: distortion, counterfeiting, detection; Theory: perfect and computational security. Offered in alternate years.

Data manipulation, analysis, and visualization. Statistical modeling, dimension reduction and techniques of supervised and unsupervised learning. Big data software technologies. Prerequisites: A grade of C- or better in CSCI 61 or equivalent, and MATH 53 and MATH 122, or permission of the instructor.

Introduction to machine learning. Selected topics from supervised and unsupervised learning. Recommendations. Current applications and technologies in machine learning development. Offered in alternate years. Prerequisites: MATH 53 and 122 and CSCI 61, all with a grade C- or better, or consent of the instructor. CSCI 183 is highly recommended.

Advanced topics in algebra, geometry, or analysis. Research projects. May be repeated for credit.

Research project supervised by a faculty member in the department. Permission of the professor directing the research must be secured before registering for this course.

Survey of randomized algorithms for basic problems in computer science such as sorting, finding the median, universal hashing, verifying polynomial identities, primality testing and prime number generation. Relevant probabilistic concepts underlying the design and analysis of these algorithms will be covered. Prerequisite, CSCI 163 or equivalent.

Guided study related to off-campus practical work experience in computer science. Enrollment restricted to majors or minors of the department. Prerequisite: Approval of a faculty sponsor.

Reading and investigation for superior students under the direction of a staff member. This can be used only to extend, not to duplicate, the content of other courses. May be repeated for credit.