Description: Calculus of algebraic, logarithmic, exponential, and trigonometric functions and their inverses. The definite integral, the fundamental theorem of calculus, geometric and physical applications including areas, volumes, work, and arc length. Techniques of integration including substitution rule, integration by parts, trigonometric substitution, partial fractions. Improper integrals.This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.This course cannot be taken for credit after completing MTH 143 or 162. Students who want to repeat a course for a grade need to secure the approval of the Dean by completing an online Repeat Course Request Form.

Description: Calculus of algebraic, logarithmic, exponential, and trigonometric functions and their inverses. The definite integral, the fundamental theorem of calculus, geometric and physical applications including areas, volumes, work, and arc length. Techniques of integration including substitution rule, integration by parts, trigonometric substitution, partial fractions. Improper integrals.This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.This course cannot be taken for credit after completing MTH 143 or 162. Students who want to repeat a course for a grade need to secure the approval of the Dean by completing an online Repeat Course Request Form.

Description: This is the third semester of a three-semester calculus sequence. Calculus with parametric curves and polar coordinates. Sequences, series, tests for convergence including comparison tests, integral test, alternating series test, ratio test, root test. Taylor and Maclaurin series. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time. This course cannot be taken for credit after completing MTH 162. Students who want to repeat a course for a grade need to secure the approval of the Dean by completing an online Repeat Course Request Form.

Description: This is the third semester of a three-semester calculus sequence. Calculus with parametric curves and polar coordinates. Sequences, series, tests for convergence including comparison tests, integral test, alternating series test, ratio test, root test. Taylor and Maclaurin series. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time. This course cannot be taken for credit after completing MTH 162. Students who want to repeat a course for a grade need to secure the approval of the Dean by completing an online Repeat Course Request Form.

Description: Passing the course will grant a waiver to the MTH 150 requirement for the Computer Science program, but does not fulfill any other requirements that MTH 150 may fulfill.This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Techniques of integration, improper integrals, applications to geometry and physics. Infinite series, Taylor series in one variable. Plane curves, parametric equations, polar coordinates, arc length. NOTE: Either MTH 164 or 165 can be taken after MTH 162 or 143. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time. Students can drop from MTH 162 to MTH 142 up to one week following the first exam in MTH 162. Interested students should speak with their professor for details. This course cannot be taken for credit after completing MTH 143. Students who want to repeat a course for a grade need to secure the approval of the Dean by completing an online Repeat Course Request Form.

Description: Techniques of integration, improper integrals, applications to geometry and physics. Infinite series, Taylor series in one variable. Plane curves, parametric equations, polar coordinates, arc length. NOTE: Either MTH 164 or 165 can be taken after MTH 162 or 143. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time. Students can drop from MTH 162 to MTH 142 up to one week following the first exam in MTH 162. Interested students should speak with their professor for details. This course cannot be taken for credit after completing MTH 143. Students who want to repeat a course for a grade need to secure the approval of the Dean by completing an online Repeat Course Request Form.

Description: Techniques of integration, improper integrals, applications to geometry and physics. Infinite series, Taylor series in one variable. Plane curves, parametric equations, polar coordinates, arc length. NOTE: Either MTH 164 or 165 can be taken after MTH 162 or 143. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time. Students can drop from MTH 162 to MTH 142 up to one week following the first exam in MTH 162. Interested students should speak with their professor for details. This course cannot be taken for credit after completing MTH 143. Students who want to repeat a course for a grade need to secure the approval of the Dean by completing an online Repeat Course Request Form.

Description: Equations of lines and planes, quadric surfaces, space curves, partial derivatives, linear approximation, directional derivatives, extrema, Lagrange multipliers, double/triple integrals including cylindrical and spherical coordinates. Line, surface, and volume integrals, divergence theorem, Stokes' theorem. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 164. MTH 162 and 164 cannot be taken concurrently. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Equations of lines and planes, quadric surfaces, space curves, partial derivatives, linear approximation, directional derivatives, extrema, Lagrange multipliers, double/triple integrals including cylindrical and spherical coordinates. Line, surface, and volume integrals, divergence theorem, Stokes' theorem. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 164. MTH 162 and 164 cannot be taken concurrently. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Equations of lines and planes, quadric surfaces, space curves, partial derivatives, linear approximation, directional derivatives, extrema, Lagrange multipliers, double/triple integrals including cylindrical and spherical coordinates. Line, surface, and volume integrals, divergence theorem, Stokes' theorem. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 164. MTH 162 and 164 cannot be taken concurrently. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Matrix algebra and inverses, Gaussian elimination, determinants, vector spaces, eigenvalue problems. First order differential equations, linear second order differential equations with constant coefficients, undetermined coefficients, linear systems of differential equations. Applications to physical, engineering, and life sciences. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 165. MTH 162 and 165 cannot be taken concurrently. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Matrix algebra and inverses, Gaussian elimination, determinants, vector spaces, eigenvalue problems. First order differential equations, linear second order differential equations with constant coefficients, undetermined coefficients, linear systems of differential equations. Applications to physical, engineering, and life sciences. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 165. MTH 162 and 165 cannot be taken concurrently. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Matrix algebra and inverses, Gaussian elimination, determinants, vector spaces, eigenvalue problems. First order differential equations, linear second order differential equations with constant coefficients, undetermined coefficients, linear systems of differential equations. Applications to physical, engineering, and life sciences. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 165. MTH 162 and 165 cannot be taken concurrently. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Matrix algebra and inverses, Gaussian elimination, determinants, vector spaces, eigenvalue problems. First order differential equations, linear second order differential equations with constant coefficients, undetermined coefficients, linear systems of differential equations. Applications to physical, engineering, and life sciences. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 165. MTH 162 and 165 cannot be taken concurrently. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Covers the material of MTH 161-165 in greater depth from the standpoint of both theory and applications. Students completing this sequence successfully will have met the requirements of MTH 235 and can begin taking upper-level courses immediately. Credit: 5 hours for each course in the 171-174 sequence. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Note: The honors calculus sequence regulation requires that students earn at least a B- in honors calculus to continue to the next course in sequence.

Description: Credit: 5 hours for each course in this sequence. An honors sequence covering the material of MTH 161-165 in greater depth from the standpoint of both theory and applications. Students completing this sequence successfully will have met the requirements of MTH 235 and can begin taking upper-level courses immediately.This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: General techniques and approaches to solving difficult nonstandard problems such as those on the Putnam examination.

Description: Techniques and methods of proof used in mathematics and computer science. Logical reasoning, mathematical induction, relations, functions. Applications to group theory or real analysis.A significant focus of this course is developing proof writing skills, which are central to the transition to higher mathematics. This course partially satisfies the upper-level writing requirement in mathematics. Students cannot take MTH 200W for credit after completion of MTH 172 or 235. Students wishing an exception can petition the mathematics department undergraduate committee by emailing mathdugs@lists.rochester.edu.

Description: Techniques and methods of proof used in mathematics and computer science. Logical reasoning, mathematical induction, relations, functions. Applications to group theory or real analysis.A significant focus of this course is developing proof writing skills, which are central to the transition to higher mathematics. This course partially satisfies the upper-level writing requirement in mathematics. Students cannot take MTH 200W for credit after completion of MTH 172 or 235. Students wishing an exception can petition the mathematics department undergraduate committee by emailing mathdugs@lists.rochester.edu.

Prerequisites: MTH 162 or equivalent, MTH 164 recommended. Same as STT 201.

Description: Probability spaces; combinatorial problems; random variables and expectations; discrete and continuous distributions; generating functions; independence and dependence; binomial, normal, and Poisson laws; laws of large numbers. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 201. MTH 162 and 201 cannot be taken concurrently.This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Prerequisites: MTH 162 or equivalent, MTH 164 recommended. Same as STT 201.

Description: Probability spaces; combinatorial problems; random variables and expectations; discrete and continuous distributions; generating functions; independence and dependence; binomial, normal, and Poisson laws; laws of large numbers. MTH 162 (or equivalent) is a strict prerequisite and must be completed before taking 201. MTH 162 and 201 cannot be taken concurrently.This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Prerequisites: MTH 201

Description: Principles of statistical estimation and inference, point and interval estimation. Maximum likelihood method for estimation and inference. Tests of hypotheses and confidence intervals, multivariate normal distribution, linear hypotheses, contingency tables, and related topics.

Description: Linear and nonlinear programming, simplex method, duality theory, sensitivity analysis, shipping and assignment problems, Karmakar's algorithm, genetic algorithms, game theory, genetic algorithms, flow problems.

Description: Mathematical concepts and techniques underlying finance theory; arbitrage pricing theory and option pricing. Finance track and FEC students should take FIN 205/206 before MTH 210. Other students can seek instructor permission.

Description: Honors version of MTH 210.

Description: Fractal geometry with applications to chaos theory and related computer software.

Description: Divisibility, primes, congruences, quadratic residues and quadratic reciprocity, primitive roots, and selected topics, with applications to cryptography and computer science.

Description: Finite-dimensional vector spaces over R and C axiomatically and with coordinate calculations. Forms, linear transformations, matrices, eigenspaces, inner products.This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Description: Finite-dimensional vector spaces over R and C axiomatically and with coordinate calculations. Forms, linear transformations, matrices, eigenspaces, inner products.This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

Cross-listed with MATH 235-1

Description: Writing intensive version of MATH 235-1

Cross-listed with MATH 235-2

Description: Writing intensive version of MATH 235-2

Description: Continuation of MTH 236 covering field theory and Galois theory including proofs of the impossibility of trisecting angles, doubling the cube, squarng the circle, and solving 5th-degree polynomials'.

Description: Permutations and combinations; enumeration through recursions and generating functions; Polya's theory of counting; finite geometrics and block designs; counting in graphs.

Description: Torsion, curvature; curves and surfaces in 3-space.

Description: Real number system, continuity and uniform continuity, mean value theorems, bounded variation, Riemann-Stieltjes integral, sequences of functions.

Description: Real number system, continuity and uniform continuity, mean value theorems, bounded variation, Riemann-Stieltjes integral, sequences of functions.

Description: Honors version of MTH 265.

Cross-listed with MATH 265H-1

Description: Writing intensive version of MATH 265H-1

Cross-listed with MATH 265-1

Description: Writing intensive version of MATH 265-1

Cross-listed with MATH 265-2

Description: Writing intensive version of MATH 265-2

Description: The numerical solution to mathematical problems by computer: linear systems, approximation, integration, and differential equations; floating point arithmetic and consequent pitfalls of computation.

Registration for Independent Study courses needs to be completed thru the instructions for online independent study registration.

Registration for Independent Study courses needs to be completed thru the instructions for online independent study registration.

Registration for Independent Study courses needs to be completed thru the instructions for online independent study registration.

Registration for Independent Study courses needs to be completed thru the instructions for online independent study registration.

Description: Rings and modules, group theory, fields and Galois theory.

Description: The first half of the course will study the general topological notions of topological space, metric spaces, quotient spaces, connectedness, compactness, manifolds and topological groups.

The second half of the course will be an introduction to the differential topology of smooth manifolds.
Topics include Sard’s theorem, transversality, intersection theory and applications such as the Jordan-Brouwer separation theorem, the Borsuk-Ulam theorem and the Poincare-Hopf theorem. This course will not cover the theory of differential forms, distributions or integration on manifolds which is usually covered in our spring graduate differentiable manifolds course instead.

Description: The combinatorial structure of complexes and the homology of polyhedra; applications of algebraic techniques in topology to classification of surfaces, fixed point theory, and analysis.

Description: Lebesgue measure on the line; measure spaces; integration; convergence theorems; Radon-Nikodym theorem; differentiation; Fubini's theorem; function spaces.

Description: This course is a requirement for math Ph.D. students during their first fall in the Ph.D. program. The course will advise them on various aspects of their professional development. It will address:a) Research practices and development: Creating a CV, creating a professional webpage, milestones for grad school, grants and funding, conferences.b) Teaching: Responsibilities, techniques, etc.c) Community: Attendance of colloquia, seminars, meeting with faculty, etc.d) Other: Discussion of arXiv, math-sci net, latex, peer support network, etc.

Description: Students will attend a selection of research talks and colloquia on current research in Mathematics. Required of math Ph.D. students during their 2nd fall in the Ph.D. program