## Mathematics : Courses

#### MTH 115 Survey of Algebra and Trigonometry

Lecture**Credits:**4

**Semester(s):**Fall, Spring

**Grading:**Graded (A-F)

A pre-calculus course; covers topics from the NYS Regents Course III: order, absolute value, inequalities, exponents, radicals, polynomials, rational expressions, solving systems of linear equations, quadratic equations and inequalities, functions (rational, logarithmic, exponential, trigonometric), graphing, trigonometric identities. Emphasizes applications to problems. This fast-paced course reviews Course III and prepares students for further courses in mathematics. Students with three years of high school math but with weak algebra skills should take ULC 147 before MTH 115. Students who have had only two years of high school mathematics may take MTH 115, or may prefer to take a two-semester sequence covering this material more thoroughly and at a more moderate pace: ULC 147 and ULC 148.

Recitation

**Credits:**1

**Semester(s):**(No information on typically offered semesters)

**Grading:**Graded (A-F)

#### MTH 120 Selected Topics in Calculus

Tutorial**Credits:**1-3

**Semester(s):**Fall, Spring, Summer

**Grading:**Graded (A-F)

Allows transfer students to efficiently learn specific topics from UB calculus courses that were not covered in calculus courses they took at other institutions.

#### MTH 121 Survey of Calculus and Its Applications I

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH 115 or Regents Course III Required for Registration

**Grading:**Graded (A-F)

For students in social, biological, and management sciences. Limits, continuity, differentiation of algebraic and exponential functions; applications; introduces integration. This course is a controlled enrollment (impacted) course. Students who have previously attempted the course and received a grade other than W may repeat the course in the summer or winter; or only in the fall or spring semester with a petition to the College of Arts and Sciences Deans' Office.

#### MTH 122 Survey of Calculus and Its Applications II

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH 121 or MTH 141

**Grading:**Graded (A-F)

Continuation of MTH 121. Maximization of functions of several variables using both calculus and elementary linear programming techniques. Elementary integration, simple differential equations, matrix algebra.

#### MTH 131 Mathematical Analysis for Management

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH 115 or Regents Course III Required for Registration

**Grading:**Graded (A-F)

For students in Management. Limits, continuity, differentiation of algebraic and exponential functions. Applications, partial derivatives and applications. Introduces integration. This course is a controlled enrollment (impacted) course. Students who have previously attempted the course and received a grade other than W may repeat the course in the summer or winter; or only in the fall or spring semester with a petition to the College of Arts and Sciences Deans' Office.

#### MTH 141 College Calculus I

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH 115 or Trigonometry or Regents Course III Required for Registration

**Grading:**Graded (A-F)

Beginning of a three-semester sequence in calculus for students of mathematics, natural sciences, and engineering. Covers differentiation and integration with applications. This course is a controlled enrollment (impacted) course. Students who have previously attempted the course and received a grade other than W may repeat the course in the summer or winter; or only in the fall or spring semester with a petition to the College of Arts and Sciences Deans' Office.

#### MTH 142 College Calculus 2

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH 141

**Grading:**Graded (A-F)

Differentiation and integration of transcendental functions; infinite sequences; series and power series; integration methods; additional topics in analytic geometry. This course is a controlled enrollment (impacted) course. Students who have previously attempted the course and received a grade other than W may repeat the course in the summer or winter; or only in the fall or spring semester with a petition to the College of Arts and Sciences Deans' Office.

Recitation

**Credits:**1

**Semester(s):**(No information on typically offered semesters)

**Grading:**Graded (A-F)

This course is a controlled enrollment (impacted) course. Students who have previously attempted the course and received a grade other than W may repeat the course in the summer or only in the fall or spring semester with a petition to the College of Arts and Sciences Deans' Office.

#### MTH 153 Honors Calculus I

Lecture**Credits:**4

**Semester(s):**Fall

**Pre-requisites:**Permission of Instructor or 4/5 on AP Calculus Required for Registration

**Grading:**Graded (A-F)

First course in the honors sequence for intended math majors or for others with suitable preparation. Emphasizes proofs and concepts of calculus. Note: Credit will not be given for both MTH 153 and MTH 121/131/141. Credit for MTH 153 may be given in addition to AP Calculus credit for MTH 141.

#### MTH 154 Honors Calculus 2

Lecture**Credits:**4

**Semester(s):**Spring

**Pre-requisites:**MTH 153

**Grading:**Graded (A-F)

A more theoretically oriented version of College Calculus II. Differentiation and integration of transcendental functions; infinite sequences; series and power series; integration methods. Topics enhance those of MTH 142 and concepts are often developed with proofs. This is designed to be a challenging course for bright students, including students who might be interested in graduate work in the sciences, engineering, and mathematics. Note: Credit for MTH 154 may be given in addition to AP Calculus credit for MTH 142. Credit will not be given for both MTH 154 and MTH 122/142. Pre-Requisite: A 4 or 5 on an AP Calculus Exam or an outstanding performance in MTH 141 College Calculus I. Contact the Math Undergraduate Office or the Honors College for registration in this course.

#### MTH 191 Introduction to Discrete Mathematics I

Lecture**Credits:**4

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**Working Knowledge of a Programming Lanugage Required for Registration

**Grading:**Graded (A-F)

First part of a two-semester sequence. Provides the mathematical foundations for the study of computer science. Also approved for mathematics majors in Concentration GS/ED. Topics include sets, relations, functions, mathematical induction, fundamental counting methods, difference equations, and sequences and series.

#### MTH 192 Introduction to Discrete Mathematics II

Lecture**Credits:**4

**Semester(s):**Spring

**Pre-requisites:**MTH 191 or CSE 191

**Grading:**Graded (A-F)

Second part of a two-semester sequence. Provides the mathematical foundations for the study of computer science. Topics include discrete probability, mathematical logic, linear algebra, and graph theory. Same as CSE 192.

#### MTH 241 College Calculus 3

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH 142 or MTH 154

**Grading:**Graded (A-F)

Geometry and vectors of n-dimensional space; Green's theorem, Gauss theorem, Stokes theorem; multidimensional differentiation and integration; application to 2- and 3-D space. This course is a controlled enrollment (impacted) course. Students who have previously attempted the course and received a grade other than W may repeat the course in the summer or winter; or only in the fall or spring semester with a petition to the College of Arts and Sciences Deans' Office.

#### MTH 251 Honors Calculus 3

Lecture**Credits:**4

**Semester(s):**Fall

**Pre-requisites:**MTH 154

**Grading:**Graded (A-F)

Third-semester calculus course for honors students and students with an excellent record in previous calculus courses. Emphasizes proofs and concepts of calculus.

#### MTH 306 Introduction to Differential Equations

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH 142 or MTH 154

**Grading:**Graded (A-F)

Analytic solutions, qualitative behavior of solutions to differential equations. First-order and higher-order ordinary differential equations, including nonlinear equations. Covers analytic, geometric, and numerical perspectives as well as an interplay between methods and model problems. Discusses necessary matrix theory and explores differential equation models of phenomena from various disciplines. Uses a mathematical software system designed to aid in the numerical and qualitative study of solutions, and in the geometric interpretation of solutions.

#### MTH 309 Introductory Linear Algebra

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH 142 or MTH 154

**Grading:**Graded (A-F)

Linear equations, matrices, determinants, vector spaces, linear mappings, inner products, eigenvalues, eigenvectors.

#### MTH 311 Introduction to Higher Mathematics

Lecture**Credits:**4

**Semester(s):**Fall, Spring

**Pre-requisites:**MTH 241 or Permission of Instructor

**Grading:**Graded (A-F)

Develops the student's ability to read, comprehend and construct rigorous proofs. Topics may include the following: the number systems N, Z, Q, R and the existence of irrational numbers; sets and functions; size of sets(finite/infinite, countable/uncountable); the countability of the rationals and the uncountability of the real numbers; boundedness; upper and lower bounds; lub's and glb's; lub and glb property; density of the rationals in the reals; Archimedean property of the reals; mathematical induction, including strong induction and the well-ordering of the natural numbers; sequences of real numbers, including the Monotone Convergence Theorem, Cauchy sequences, and the Bolzano-Weierstrass Theorem.

#### MTH 313 Elements of Set Theory

Lecture**Credits:**4

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 241

**Grading:**Graded (A-F)

Cardinals, ordinals, order-types, and operations on them. Axiom of choice. Sets.

#### MTH 335 Elements of Geometry

Lecture**Credits:**4

**Semester(s):**Spring

**Pre-requisites:**MTH 309

**Grading:**Graded (A-F)

Euclidean and non-Euclidean geometries. Studies the Hilbert postulates and various models, emphasizing Euclidean and Lobachevskian geometries.

#### MTH 337 Introduction to Scientific and Mathematical Computing

Lecture**Credits:**4

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 141 and MTH 142 or MTH 154

**Grading:**Graded (A-F)

Computing now plays an essential and ever-expanding role in science and mathematics. This course provides a broad introduction to computing in the sciences and in both abstract and applied mathematics. It is accessible to students early in their undergraduate program, thereby opening the door to the profitable use of computation throughout the junior and senior years.

#### MTH 338 Data-Oriented Computing for Mathematics

Lecture**Credits:**4

**Semester(s):**Fall, Spring, Summer

**Pre-requisites:**MTH241LLB & MTH337LLB

**Grading:**Graded (A-F)

A practical hands-on introduction for mathematics majors to tools and methods for acquiring, storing, manipulating, and exploring data - both big and small. It also introduces students to the use of data in a variety of fields where mathematical talent can be productively applied: examples are bioinformatics (e.g. genomics), health care informatics, urban and regional planning, and data journalism. Extensive writing of reports is a central feature of the course.

#### MTH 353 Introduction to Combinatorics I

Lecture**Credits:**3

**Semester(s):**Fall

**Pre-requisites:**MTH 241

**Grading:**Graded (A-F)

Permutations, combinations, and other problems of selecting and arranging objects subject to various restrictions; generating functions; recurrence relations; inclusion-exclusion theorem.

#### MTH 354 Introduction to Combinatorics II

Lecture**Credits:**3

**Semester(s):**Spring

**Pre-requisites:**MTH 241

**Grading:**Graded (A-F)

Theory of graphs: Eulerian and Hamiltonian circuits; trees; planarity; colorability; directed graphs and tournaments; isomorphism; adjacency matrix; applications to problems in communication, scheduling, and traffic flow.

#### MTH 399 Junior Seminar

Seminar**Credits:**1-3

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 241 and Permission of Instructor Required for Registration

**Grading:**Graded (A-F)

Seminar based around a specific topic or area of mathematics appropriate to juniors in mathematics and the mathematical sciences. the format is determined by the instructor or team of instructors. Sessions include lectures by UB faculty in Mathematics and other departments around the university, talks by outside experts presentations by the students registered in the seminar on readings and/or research work they have done in relation to the subject matter of the seminar, and occasional field trips. Open discussion during the sessions is a key feature.

#### MTH 411 Probability Theory

Lecture**Credits:**4

**Semester(s):**Fall, Spring

**Pre-requisites:**MTH 141 and MTH 142 or MTH 154

**Grading:**Graded (A-F)

A first course in probability. Introduces the basic concepts of probability theory and addresses many concrete problems. A list of basic concepts includes axioms of probability, conditional probability, independence, random variables (continuous and discrete), distribution functions, expectation, variance, joint distribution functions, limit theorems.

#### MTH 412 Introduction to Statistical Inference

Lecture**Credits:**4

**Semester(s):**Fall

**Pre-requisites:**MTH 411

**Grading:**Graded (A-F)

Topics include: review of probability, conditional probability, Bayes' Theorem; random variables and distributions; expectation and properties; covariance, correlation, and conditional expectation; special distributions; Central Limit Theorem and applications; estimations, including Bayes; estimators, maximum likelihood estimators, and their properties. Includes use of sufficient statistics to improve estimators, distribution of estimators, unbiasedness, hypothesis testing, linear statistical models, and statistical inference from the Bayesian point of view.

#### MTH 413 Introduction to Mathematical Logic I

Lecture**Credits:**3

**Semester(s):**Fall

**Pre-requisites:**MTH 313

**Grading:**Graded (A-F)

Informal and formal development of propositional calculus; predicate calculus and predicate calculus with equality; completeness theorem and some consequences.

#### MTH 417 Survey of Multivariable Calculus

Lecture**Credits:**4

**Semester(s):**Fall, Spring

**Pre-requisites:**MTH 241

**Grading:**Graded (A-F)

For math majors in Concentration C, and majors of science and engineering. Surveys functions of several variables; differentiation, composite, and implicit functions; critical points; line integrals; Green's theorem. Vector field theory; gradient, divergence, and curl; integral theorems. Introduces functions of a complex variable; curves and regions in the complex plane; analytic functions, Cauchy-Riemann equations, Cauchy integral formula. Applications.

#### MTH 418 Survey of Partial Differential Equations

Lecture**Credits:**4

**Semester(s):**Fall, Spring

**Pre-requisites:**MTH 241 and MTH 306

**Grading:**Graded (A-F)

Surveys elementary differential equations of physics; separation of variables and superposition of solutions; orthogonal functions and Fourier series. Introduces boundary value problems, Fourier and Laplace transforms.

#### MTH 419 Introduction to Abstract Algebra

Lecture**Credits:**4

**Semester(s):**Fall, Spring

**Pre-requisites:**MTH 309, also MTH 311 Recommended

**Grading:**Graded (A-F)

A theoretical introduction to the basic ideas of modern abstract algebra. Topics include groups, rings, fields, quotient groups and rings, and the fundamental homomorphism theorems. Also may include applications to number theory.

#### MTH 420 Advanced Linear Algebra

Lecture**Credits:**4

**Semester(s):**Spring

**Pre-requisites:**MTH 309, also MTH 311 recommended

**Grading:**Graded (A-F)

Topics in advanced linear algebra.

#### MTH 425 Introduction to Complex Variables I

Lecture**Credits:**3

**Semester(s):**Spring

**Pre-requisites:**MTH 241

**Grading:**Graded (A-F)

For students of physics, electrical and other areas of engineering, and mathematics. Analyticity; calculus over the complex numbers. Cauchy theorems, residues, singularities, conformal mapping. Weierstrass convergence theorem; analytic continuation.

#### MTH 426 Introduction to Complex Variables II

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 425

**Grading:**Graded (A-F)

Continuation of MTH 425. Weierstrass and Mittag-Leffler theorems, harmonic functions, conformal mapping and Green's function, analytic equivalence, and Riemann's mapping theorem. Montel's theorem, external mappings.

#### MTH 428 Introduction to Topology II

Lecture**Credits:**4

**Semester(s):**Spring

**Pre-requisites:**MTH 427

**Grading:**Graded (A-F)

Homotopy and homotopy equivalence. Fundamental group. Covering spaces and their classification. Seifert-van Kampen theorem. CW complexes and their fundamental groups. Topological manifolds.

#### MTH 429 Introduction to the Theory of Numbers I

Lecture**Credits:**3

**Semester(s):**Fall

**Pre-requisites:**MTH 311 Recommended

**Grading:**Graded (A-F)

The Euclidean algorithm and unique factorization; arithmetical functions; congruences, reduced residue systems; primitive roots; certain diophantine equations.

#### MTH 430 Introduction to the Theory of Numbers II

Lecture**Credits:**3

**Semester(s):**Spring

**Pre-requisites:**MTH 429

**Grading:**Graded (A-F)

Continuation of MTH 429. Irrational numbers; continued fractions from a geometric viewpoint; best rational approximations to real numbers; the Fermat-Pell equation; quadratic fields and integers. Applications to diophantine equations.

#### MTH 431 Introduction to Real Variables I

Lecture**Credits:**4

**Semester(s):**Fall, Spring

**Pre-requisites:**MTH 311

**Grading:**Graded (A-F)

Comprehensive and rigorous course in the study of real valued functions of one real variable. Topics include sequences of numbers, limits and the Cauchy criterion, continuous functions, differentiation, inverse function theorem, Riemann integration, sequences and series, uniform convergence. A prerequisite for most advanced courses in analysis.

Laboratory

**Credits:**4

**Semester(s):**Fall, Spring

**Grading:**Graded (A-F)

Comprehensive and rigorous course in the study of real valued functions of one real variable. Topics include sequences of numbers, limits and the Cauchy criterion, continuous functions, differentiation, inverse function theorem, Riemann integration, sequences and series, uniform convergence. A prerequisite for most advanced courses in analysis.

#### MTH 432 Introduction to Real Variables II

Lecture**Credits:**4

**Semester(s):**Spring

**Pre-requisites:**MTH 431

**Grading:**Graded (A-F)

Rigorous course in analyzing dimensions greater than one. Includes details of three basic theorems: the inverse function theorem, the implicit function theorem, and the change of variables theorem in multiple integrals. Topics include continuously differentiable functions, the chain rule, inverse and implicit function theorems, Riemann integration, partitions of unity, change of variables theorem.

#### MTH 435 Introduction to Cryptography

Lecture**Credits:**3

**Semester(s):**Fall

**Pre-requisites:**MTH 419 or MTH 429

**Grading:**Graded (A-F)

Explains the basics of cryptography, which is the systematic study of methods of concealing messages from people who are not authorized to read them. Topics include the following: cryptosystem definitions and basic types of attack; substitution ciphers. Hill ciphers; congruences and modular exponentiation; digital encryption standard; public key and RSA cryptosystems; pseudoprimes and primality testing; Pollard rho method; basic finite field theory; discrete log; and digital signatures.

#### MTH 437 Introduction to Numerical Analysis I

Lecture**Credits:**4

**Semester(s):**Fall

**Pre-requisites:**CSE 113 or CSE 115 or MTH 337 and MTH 241 and MTH 306 and MTH 309

**Grading:**Graded (A-F)

First part of a 2-semester sequence which explores the design and implementation of numerical methods to solve the most common types of problem arising in science and engineering. Most such problems cannot be solved in terms of a closed analytical formula, but many can be handled with numerical methods learned in this course. Topics for the two semesters include: how a computer does arithmetic, solving systems of simultaneous linear or nonlinear equations, finding eigenvalues and eigenvectors of (large) matrices, minimizing a function of many variables, fitting smooth functions to data points (interpolation and regression), computing integrals, solving ordinary differential equations (initial and boundary value problems), and solving partial differential equations of elliptic, parabolic, and hyperbolic types. We study how and why numerical methods work, and also their errors and limitations. Students gain practical experience through course projects that entail writing computer programs.

#### MTH 438 Introduction to Numerical Analysis II

Lecture**Credits:**4

**Semester(s):**Spring

**Pre-requisites:**MTH 437 or CSE 437

**Grading:**Graded (A-F)

Second part of the 2-semester sequence described under MTH 437.

#### MTH 443 Fundamentals of Applied Mathematics I

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 241, MTH 306, and MTH 309

**Grading:**Graded (A-F)

Mathematical formulation and analysis of models for phenomena in the natural sciences. Includes derivation of relevant differential equations from conservation laws and constitutive relations. Potential topics include diffusion, stationary solutions, traveling waves, linear stability analysis, scaling and dimensional analysis, perturbation methods, variational and phase-space methods, kinematics, and laws of motion for continuous media. Examples from areas might include, but are not confined to, biology, fluid dynamics, elasticity, chemistry, astrophysics, geophysics.

#### MTH 444 Fundamentals of Applied Mathematics II

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Pre-Requistie: MTH 241, MTH 306, and MTH 309

**Grading:**Graded (A-F)

Explores other topics described in MTH 443.

#### MTH 455 Mathematical Modeling

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 306 and MTH 309

**Grading:**Graded (A-F)

Introduces the use of mathematical modeling in applied mathematics using a case study approach. Population ecology; chemical kinetics; traffic dynamics.

#### MTH 458 Mathematical Finance

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 241

**Co-requisites:**MTH 306

**Grading:**Graded (A-F)

Introduces the mathematical theory and computation of modern financial products used in the banking and corporate world. Derives and analyzes mathematical models for the valuation of derivative products.

#### MTH 459 Mathematical Finance 2

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 458

**Grading:**Graded (A-F)

Describes the mathematical development of both the theoretical and the computational techniques used to analyze financial instruments. Specific topics include utility functions; forwards, futures, and swaps; and modeling of derivatives and rigorous mathematical analysis of the models, both theoretically and computationally. Develops, as needed, the required ideas from partial differential equations and numerical analysis.

#### MTH 460 Theory of Games

Lecture**Credits:**4

**Semester(s):**(No information on typically offered semesters)

**Pre-requisites:**MTH 241 and MTH 309

**Grading:**Graded (A-F)

Introduces the mathematical theory of games--a systematic approach to modeling conflict, competition, cooperation, and negotiation--with applications to mathematics, economics, politics and evolutionary biology. A game, in mathematical terms, consists of a starting point and various choices made by 'players.' Each choice might lead to new choices or to an outcome that ends the game. Some choices might be random; some might be made without full information about what has transpired. The players are each trying to maximize their own payoff, but the play of each might influence the results of the others. The approaches Game Theory uses to analyze conflict between two or more people lead to results that can seem paradoxical as well as illuminating. The most important thing a student can take from this course is a useful way of approaching decisions, from the trivial-- how does a couple decide which movie to see--to the critical--how should countries pursue their goals in cooperation or conflict with their allies and enemies. Partial list of topics: Prisoner's Dilemma, game trees, pure and mixed strategies, backward induction, normal form, Nash equilibrium, chance moves, utility functions, domination, convexity, payoff regions, strictly competitive games, separating hyperplanes, repeating games, and cooperative bargaining theory.

#### MTH 461 Topics in Algebra

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments pertaining to a specific area of algebra. Topics courses can be taken more than once for credit.

#### MTH 462 Topics in Analysis

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments pertaining to analysis. Topics courses can be taken more than once for credit.

#### MTH 463 Topics in Applied Mathematics

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments pertaining applied mathematics. Topics courses can be taken more than once for credit.

#### MTH 464 Topics in Combinatorial Analysis

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments pertaining combinatorial analysis. Topics courses can be taken more than once for credit.

#### MTH 465 Lectures in Geometry

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Provides a broader understanding of differential geometry. Comprehensively introduces the theory of curves and surfaces in space. Moves toward the goal of viewing surfaces as special concrete examples of differentiable manifolds, reached by studying surfaces using tools that are basic to studying manifolds. Topics include curves in 3-D space, differential forms, Frenet formulae, patch computations, curvature, isometries, intrinsic geometry of surfaces. Serves as an introduction to more advanced courses involving differentiable manifolds.

#### MTH 466 Topics in Logic and Set Theory

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments pertaining logic and set theory. Topics courses can be taken more than once for credit.

#### MTH 467 Topics in Number Theory

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments pertaining number theory. Topics courses can be taken more than once for credit.

#### MTH 468 Topics in Numerical Analysis

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments pertaining numerical analysis. Topics courses can be taken more than once for credit.

#### MTH 469 Topics in Topology

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Instructor Required to Register

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments pertaining topology. Topics courses can be taken more than once for credit.

#### MTH 470 Topics in Mathematics

Lecture**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Variable (Set by Instructor)

**Grading:**Graded (A-F)

Treats problems, methods, and recent developments in any area of mathematics that does not fit nearly or fully under the title of any other "Topics in..." course.

#### MTH 495 Undergraduate Supervised Teaching

Tutorial**Credits:**3

**Semester(s):**(No information on typically offered semesters)

**Requisites:**Permission of Department

**Grading:**Pass/Fail

Students who have at least junior status and satisfy the department's pre-requisites may apply to serve as undergraduate teaching assistants in one of the calculus courses (MTH 121/MTH 122, MTH 131, MTH 141/MTH 142, MTH 241). Under the supervision of the professor, undergraduate teaching assistants will lead two recitation sections each week of approximately 30 students each. Some grading of homework will be expected.

#### MTH 496 Internship in Mathematics

Tutorial**Credits:**1-4

**Semester(s):**Fall, Spring

**Grading:**Graded (A-F)

Students get field experience in mathematical employment,in business, industry or education, working under the joint supervision of an off-campus supervisor and a university faculty member, usually the director of undergraduate studies. May be taken once only.

#### MTH 497 Honors Thesis in Mathematics

Tutorial**Credits:**4

**Semester(s):**Fall, Spring

**Grading:**Graded (A-F)

Open only to math majors intending to seek an honors degree in mathematics. For information, consult the director of undergraduate studies in the Department of Mathematics.

#### MTH 499 Independent Study

Tutorial**Credits:**1-4

**Semester(s):**Fall, Spring

**Grading:**Graded (A-F)

Individual study arranged between student and faculty member in an area of mathematics of particular interest to the student.

Updated: 22 Jul 2015 15:30:22 EDT