## Courses

### MATH-104C P4 Mathematical Perspectvs (3)

This course is designed to bring the beauty, fun, and utility of mathematics to a broad variety of students. By use of games, puzzles, paradoxes, art, and other explorations, students gain insight into the way mathematicians think and learn ways of thinking that significantly improve their ability to solve problems. Possible topics include number theory and secret codes, notions of the infinite, geometry and topology, chaos and fractals, and probability and expectation.

Attributes: P4 YLIB### MATH-109C College Algebra (3)

Topics in this course include relations and their graphs, functions and some of their important properties, trigonometry, exponential and logarithmic models, and methods for solving systems of equations and inequalities.

Attributes: YLIB### MATH-111C SQ Finite Math Soc Sci (3)

Topics include: functions, linear and non-linear models, matrix algebra and applications, linear programming applications.

Attributes: SQ YLIB### MATH-112C P4 Calculus for Soc Sci (3)

This course is devoted to the study of calculus concepts and techniques. Emphasis is placed on differential and integral calculus. Applications to business, industry, and the social sciences are heavily stressed in the course. This course is not equivalent to MATH 120C and may not be taken concurrently with MATH 120C or if the equivalent of MATH 120C has been successfully completed.

Attributes: P4 YLIB### MATH-114C P4 Math Explorations I (3)

Course design is guided by the NCTM Standards, and therefore mathematics content will be developed through problem-solving, communication (both written and oral), reasoning, and with the objective of creating mathematical connections. Students gain an understanding of the mathematical concepts by studying patterns and making generalizations. Topics in the two-course sequence include: numeration systems (including non-decimal bases), the four basic arithmetic operations and the development of their associated algorithms, the extension of the integers and rational numbers to the real number system, mathematical modeling, number theory, proportional reasoning, measurement, geometry, probability, and statistics. MATH/MSTI 114C and MATH/MSTI 115C are a two-course mathematics content sequence designed for the prospective childhood educator. Cross-listed with MATH 114C.

Attributes: P4 YLIB### MATH-115C P4 Math Explorations II (3)

This course is a continuation of the topics included in MATH/MSTI 114C. Cross-listed with MSTI 115C.

Attributes: P4 YLIB

Pre-requisites: MATH-114C C OR MSTI-114C C### MATH-119C P4 Precalculus (4)

Topics include trigonometric functions, analytic geometry, and properties of functions, with emphasis on exponential and logarithmic functions. Graphical interpretations are emphasized throughout the course. Most topics are supported by the use of graphing calculators.

Attributes: P4 YLIB

Pre-requisites: -### MATH-120C P4 Calculus I (4)

This is a first course in calculus for mathematics and science majors. The topics include limits, derivatives, applications of the derivative, tangent lines, concavity, maxima and minima, mean value theorem, indeterminate forms, Riemann sums, fundamental theorem of calculus and applications of the definite integral.

Attributes: P4 YLIB

Pre-requisites: -### MATH-122C P4 Calculus II (4)

This is a second course in calculus, building on the material of MATH 120C. The subject matter includes techniques of integration, applications of the integral, infinite series, power series, Taylor series, and improper integrals.

Attributes: P4 YLIB

Pre-requisites: MATH-120C C### MATH-150C Elem Discrete Math (3)

This course introduces students to the mathematics that is needed for computer science. In particular, this includes sets, ordered tuples, logic, rates of growth, finite state machines, functions, composition of functions, relations, matrices as representations of digraphs, Karnaugh maps, and binary representation of data in the computers.

Attributes: YLIB

Pre-requisites: -### MATH-170 P4 Mathematical Modeling (3)

This course is designed to introduce students to various applications of mathematics utilizing relatively simple mathematics and basic technology. The course reinforces the cycle of steps in modeling real-world phenomena through the study of topics such as: difference equations, sequences of numbers, recursive relationships, and the Game of Life. It’s designed to complement the sequence of topics in Calculus I but does not use any calculus concepts.

Attributes: P4 YLIB### MATH-199C RW Research-based Writing (3)

Students learn the basics of writing an academic research paper in this discipline. Emphasis is on elements of persuasive argumentation, the inclusion of more than one perspective on an issue, the proper use and documentation of sources, and revision. Students also learn how to make an effective oral presentation of their research. Department-determined topic may change from semester to semester and is likely to include literary texts as primary materials.

Restricted to freshmen and transfers.

Note: 199C courses may not be taken for credit more than once.

Attributes: RW YLIB

Restrictions: Including: -Class: Freshman, Sophomore### MATH-200C Discrete Structures (3)

This course has a two-fold purpose: the first is to introduce the student to modern mathematics and its methods of argument and proof; the second is to make practical applications of these ideas in the fields of applied mathematics and computer science. The subject matter includes a selection from: sets, functions, relations, combinations, graphs, trees, strings, number systems, abstract structures, Boolean algebra, and the design of logical circuits. Students begin their exploration and study of proofs in mathematics.

Attributes: YLIB

Pre-requisites: MATH-120C C OR MATH-150C C### MATH-201 Math Seminar (1)

Students will focus on learning to read mathematical journal articles written at an appropriate level. This will offer an opportunity to see many different areas of mathematics and explore current, interesting problems in the discipline. During the seminar, students will also explore various careers in which mathematics plays a vital role.

Attributes: YLIB

Pre-requisites: MATH-122C C### MATH-221C Calculus III (4)

This is a course in multivariable calculus. The topics include three-dimensional coordinate geometry, vector arithmetic, visualization of multivariable functions, partial derivatives and gradients, optimization, double and triple integrals in Cartesian and other common coordinate systems, line integrals, surface integrals, and the main integral theorems of vector calculus. The course also covers applications of these concepts.

Attributes: YLIB

Pre-requisites: MATH-122C C### MATH-232 Linear Algebra (3)

The content includes linear equations, matrices, vector spaces, determinants, linear transformations, and eigenvalues.

Attributes: YLIB

Pre-requisites: MATH-122C C### MATH-260 Applied Mathematical Stats (3)

Topics studied include the binomial, Poisson, normal, t, F, and chi-square distributions and their uses; parametric tests of hypotheses and their nonparametric equivalents; regression and correlation; the analysis of variance; bootstrapping; introduction to Bayesian estimation. Statistical computing in R will be emphasized.

Attributes: HHSM YLIB

Pre-requisites: -### MATH-290 Peer Tutoring in Math (1)

This course educates students in the theory and practice of tutoring in mathematics. Students tutoring in the Math Center must be taking or have taken this course. Graded S/U. Permission of the Professor is required to register.

Attributes: YLIB### MATH-301 Mathematical Stats I (3)

The content includes probability models, finite sample spaces, conditional probability and independence, random variables, functions and sums of random variables, characterizations of random variables, and moment-generating functions.

Attributes: YLIB

Pre-requisites: MATH-122C C### MATH-302 Mathematical Statistics II (3)

As a continuation of MATH 301, this course will use the probabilistic framework developed there to develop statistical analyses. Estimation (including the method of maximum likelihood), confidence intervals, hypothesis testing, regression, and correlation are covered. Analysis of Variance and tests of categorical relationships are included, as well as an introduction to time series analysis and an introduction to Bayesian statistics.

Attributes: YLIB

Pre-requisites: MATH-301 C### MATH-310 Number Theory (3)

The following topics are covered: Euclid’s algorithm, prime numbers, perfect numbers, Diophantine equations, congruences, and other specialized applications. In addition, some of the historical background of the subject is discussed.

Attributes: YLIB

Pre-requisites: (MATH-200C C OR MATH-200 C) AND MATH-232 C### MATH-325 Abstract Algebra (3)

This is a further study of algebraic structures. The topics include groups, rings, integral domains, and fields.

Attributes: YLIB

Pre-requisites: MATH-200C C AND MATH-232 C### MATH-333 Applied Mathematics I (3)

The first of a two-semester sequence in applied mathematics for the physical sciences and engineering. The course content is derived from the following list of topics: vector calculus; tensor analysis; functions of a complex variable; solutions of partial differential equations; eigenvalue problems; Fourier series; Laplace and Fourier transforms; calculus of variations; and properties of some special functions. Cross-listed with PHYS 333.

Attributes: YLIB

Pre-requisites: MATH-221C C AND MATH-222 C### MATH-334 Applied Math II (3)

A continuation of MATH 333. Cross-listed with PHYS 334.

Attributes: YLIB

Pre-requisites: MATH-333 C OR PHYS-333 C-### MATH-391C Numerical Analysis I (3)

A study of numerical methods for solving problems, such as approximating the zeroes of non-linear equations, approximation of functions by polynomials, numerical solution of systems of equations, numerical integration, and numerical solution to differential equations. Use of the computer for application to the above problems through student-written and/or commercially available programs is examined.

Attributes: YLIB

Pre-requisites: CSCI-161 C AND MATH-222 C AND MATH-232 C### MATH-392 Numerical Analysis II (3)

In addition to an in-depth reexamination of some of the topics in MATH 391C, this course covers solutions of differential equations and systems of differential equations, matrix eigenvalue problems, and other matrix problems.

Attributes: YLIB

Pre-requisites: MATH-391C C### MATH-400 Special Topics (1 TO 3)

This course presents a special topic in mathematics that would not be offered regularly. Possible topics include: linear spaces, complex variables, general topology, and differential geometry. This course may be repeated for different topics.

Spring 2016 Topic: Introduction to Modern Cryptology We will study classical ciphers and modern public-key cryptosystems, with increasing levels of information security as an organizing theme. Mathematical topics from probability, number theory, and abstract algebra will be developed as needed and applied to the development and analysis of coding algorithms.

Attributes: YLIB

Pre-requisites: MATH-200C C

Restrictions: Including: -Major: Mathematics, Mathematics -Class: Junior, Senior### MATH-410 Probability Models (3)

This course seeks to apply the mathematical concepts learned in MATH 301 and 302 to various applied settings. Probability models will be discussed as they relate to the physical sciences, psychology, engineering, and computers. Topics will be chosen from discrete and continuous Markov chains, queueing theory, branching processes, Brownian motion, Monte Carlo methods, and applications of conditional probability.

Attributes: YLIB

Pre-requisites: MATH-301 Y C### MATH-417 Foundations of Geometry (3)

This course is a study of projective and Euclidean geometries with a special emphasis on axiom systems and the relationships between Euclidean geometry, projective geometry, and the non-Euclidean geometries.

Attributes: YLIB

Pre-requisites: MATH-200C C AND MATH-232 C### MATH-421 Principles Real Analysis I (3)

Topics covered in the two-semester sequence include: sets, functions and sequences of real numbers, limits and continuity; elementary topology of the real line; Riemann integration; differentiation and the mean value theorem; infinite series; and sequences of functions and uniform convergence.

Attributes: YLIB

Pre-requisites: MATH-221C C AND MATH-325 C### MATH-422 Prin Real Analysis II (3)

This course is a continuation of the topics included in MATH 421.

Attributes: YLIB

Pre-requisites: MATH-421 C### MATH-460 Actuarial Math Seminar (1)

This course will introduce some concepts in probability, such as joint moment generating functions and order statistics, as well as review many concepts from MATH 301 with a focus on increasing computational accuracy, speed, and understanding. Through problem solving and repeated practice, students will apply the aspects of probability from MATH 301 in a risk management context. This course is recommended for those studying for the Exam P by the Society of Actuaries.

Attributes: YLIB

Pre-requisites: MATH-301 C### MATH-461 Mathematical Finance (3)

The purpose of this course is to provide an understanding of the concepts of financial mathematics and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in reserving, valuation, pricing, asset/liability management, and other uses. The students will be given an introduction to financial instruments, including derivatives, and the concept of no arbitrage as it relates to financial mathematics. Topics will be chosen from: interest theory (such as the time value of money, annuities and cash flows, loans, bonds, and immunization), financial economics (such as derivatives, options, futures, swaps, and hedging), and mathematical models (such as finite probability spaces, Martingales and Markov processes, risk-neutral and arbitrage-free pricing theory in a complete market, binomial and trinomial tree models, and Black-Scholes analysis of European options). This class covers topics of the SOA Exam FM/CAS Exam 2.

Attributes: YLIB

Pre-requisites: MATH-301 Y D-### MATH-470 Adv Math Perspectives (3)

This course is designed to help students to connect their undergraduate mathematics experience to the high school mathematics curriculum. Concepts from number theory are integrated into the course. This class involves evaluating and critiquing mathematical arguments from across the mathematics curriculum, giving students an opportunity to analyze various logic flaws and misconceptions, and reinforcing the structure of proofs and reasoning.

Attributes: YLIB

Pre-requisites: MATH-421 C### MATH-480 Mathematics Capstone (3)

Students write and present a senior thesis involving a substantive project that demonstrates a synthesis of learning accumulated in the major on a topic from an area of mathematics. The topic chosen is approved by the course thesis advisors and the chair of the department. The student works with the thesis advisors to develop a coherent presentation of his/her chosen topic. The written thesis and its oral presentation must be at a level accessible to an audience of majors who may not have studied the topic presented. Permission of the Department Chair is required to register.

Attributes: YLIB

Restrictions: Including: -Major: Mathematics -Class: Senior### MATH-490 Internship (1 TO 3)

The student spends 10 to 15 hours per week as an intern with an organization in the Rochester area. The student performs tasks with the goal of participating meaningfully in real-world mathematical applications or research. The student keeps a daily journal and participates in a seminar to be held each semester for prospective students and supervising organizations. For an internship, a student must be a junior or senior MATH major with a GPA of 3.00 or higher in the major and be enrolled in at least one other upper-level mathematics course. There is no guarantee that there will be a sufficient number of internships to accommodate qualified students wishing to enroll in the course. Permission of the Department Chair is required to register.

Attributes: YLIB

Restrictions: Including: -Major: Mathematics -Class: Junior, Senior### MATH-496 Independent Study (1 TO 3)

Well-qualified seniors may initiate and carry out a proposal for independent, advanced work under the supervision of a member of the department. Completion of the Independent Study/Tutorial Authorization form is required. See the College Policy on Independent Study.

Attributes: YLIB

Restrictions: Including: -Class: Senior