# Undergraduate Program

## Courses

#### Courses currently being offered:

Check the course schedules/descriptions available via the Registrar's Office for the official schedules for the widest range of terms for which such information is available.

### Course Catalog

Below you will find a list of all undergraduate courses that have been offered.**NOTE: Not all of these courses are offered in any given year.**

- MTH 130 EXCURSIONS IN MATH
The nature of mathematics and its application. Emphasis on concepts and understanding rather than acquisition of techniques. Intended for concentrators in the humanities and social sciences.

*Prerequisites: None.**Last Offered: Spring 2019* - MTH 140 FOUNDATIONS OF CALCULUS
This course covers pre-calculus material and is intended for students lacking the algebra and trigonometry background necessary to perform successfully in MTH 141. After completing this course students are ready to take MTH 141. MTH140 cannot be taken after completing MTH141 or MTH161 or higher.

*Last Offered: Fall 2019* - MTH 141 CALCULUS I
Analysis of the elementary real functions: algebraic, trigonometric, exponentials and their inverses and composites. Their graphs and derivatives. Topics include limits, continuity, asymptotes, the definition of the derivative, derivatives and derivative rules for algebraic, trigonometric, exponentials, and logarithms. Implicit differentiation, related rates, linear appoximation, differentials, mean value theorem, maxima and minima, curve sketchings, l'Hospital's rule. MTH 141, 142, and 143 is a three-semester sequence that covers, at a slower pace, exactly the same material as the two-semester sequence, MTH 161 and 162. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time. This course cannot be taken for credit after completing any of MTH 141, 142, 143, 161, 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.

*Last Offered: Fall 2019* - MTH 142 CALCULUS II
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.

*Prerequisites: MTH 141**Last Offered: Fall 2019* - MTH 143 CALCULUS III
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.

*Prerequisites: MTH 141, MTH 142**Last Offered: Fall 2019* - MTH 150 DISCRETE MATHEMATICS
Logic, functions, algorithms, mathematical reasoning, mathematical induction, recurrence relations, techniques of counting, equivalence relations, graphs, trees. Required for Computer Science majors. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

*Last Offered: Fall 2019* - MTH 150A DISCRETE MATH MODULE
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.

*Prerequisites: Permission of instructor required. This module is only open to students in honors calculus.**Last Offered: Fall 2019* - MTH 161 CALCULUS IA
Elementary real functions: algebraic, trigonometric, exponential, their inverses, graphs, derivatives and integrals; limits, l'Hopital's rules, Mean value theorem, maxima and minima, curve plotting. The fundamental theorem of calculus, with geometric and physical applications, substitution rule for integration. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time. Students can drop from MTH 161 to MTH 141 up to one week following the first exam in MTH 161. Interested students should speak with their professor for details. This course cannot be taken for credit after completing any of MTH 141, 142, 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.

*Last Offered: Fall 2019* - MTH 162 CALCULUS IIA
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.

*Prerequisites: MTH 161 or equivalent**Last Offered: Fall 2019* - MTH 164 MULTIDIMENSIONAL CALCULUS
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.

*Prerequisites: MTH 143, 162, or 172.**Last Offered: Fall 2019* - MTH 165 LINEAR ALGEBRA WITH DIFFERENTIAL EQUATIONS
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.

*Prerequisites: MTH 143, 162, or MTH 172. NOTE: MTH 164 is not a prerequisite for MTH 165. Due to overlapping content, it is not recommended to take both MTH 163 and 165.**Last Offered: Fall 2019* - MTH 171 HONORS CALCULUS I
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.

*Last Offered: Fall 2019* - MTH 172 HONORS CALCULUS II
This course is a continuation of MTH 171.

*Prerequisites: MTH 171**Last Offered: Spring 2019* - MTH 173 HONORS CALCULUS III
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.

*Prerequisites: MTH 172 or permission of instructor.**Last Offered: Fall 2019* - MTH 174 HONORS CALCULUS IV
This course is a continuation of MTH 173.

*Prerequisites: MTH 173**Last Offered: Spring 2019* - MTH 190 TOPICS IN PROBLEM SOLVING
General techniques and approaches to solving difficult nonstandard problems such as those on the Putnam examination.

*Prerequisites: None.**Last Offered: Fall 2019* - MTH 199 THE INFINITE
*No description**Prerequisites: Cross-listed with PHL 199.**Last Offered: Fall 2016* - MTH 200W TRANSITION TO HIGHER MATH
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.

*Prerequisites: MTH 162 or equivalent.**Last Offered: Fall 2019* - MTH 201 INTRODUCTION TO PROBABILITY
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.**Last Offered: Fall 2019* - MTH 201H INTRO TO PROBABILITY
*No description**Last Offered: Fall 2016* - MTH 202 INTRODUCTION TO STOCHASTIC PROCESSES
Theory and applications of random processes, including Markov chains, Poisson processes, birth-and-death processes, random walks.

*Prerequisites: MTH 201. Same as STT 202.**Last Offered: Spring 2019* - MTH 203 INTRODUCTION TO MATH STATISTICS
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.

*Prerequisites: MTH 201**Last Offered: Spring 2019* - MTH 208 OPERATIONS RESEARCH I
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.

*Prerequisites: MTH 162 and 165, or 173Q**Last Offered: Fall 2019* - MTH 210 INTRODUCTION TO FINANCIAL MATHEMATICS
Mathematical concepts and techniques underlying finance theory; arbitrage pricing theory and option pricing. This course uses the Tuesday/Thursday 08:00-09:30am Common Exam time.

*Prerequisites: FIN 205 and (MTH 143 or 162) and (one of STT 211, 212, 213, ECO 230, or MTH 201).**Last Offered: Fall 2019* - MTH 210H INTRO TO FINANCIAL MATH
- MTH 215 FRACTALS & CHAOTIC DYNAMICS
Fractal geometry with applications to chaos theory and related computer software.

*Prerequisites: MTH 171 or 162 (MTH 200W recommended if you have not taken 171).**Last Offered: Fall 2017* - MTH 216 MATHEMATICAL LOGIC I
The central goal of this course is to study in depth the proof of Goedelâ€™s First Incompleteness Theorem, one of the most surprising and important results about the possibilities and limitations of first-order logic. The course will explore both the logical underpinnings of the proof and its philosophical implications. Topics covered include recursive functions, axiomatic formal systems, arithmetical definability, the arithmetization of syntax, and diagonalization.

*Last Offered: Spring 2018* - MTH 217 MATHEMATICAL MODELING IN POLITICAL SCIENCE
Elementary game theory with applications: Nash equilibria, prisoner's dilemma, chicken; measures of voting power, social choice, Arrow's Theorem. Offered fall, even years.

*Prerequisites: Some mathematical sophistication required. MTH 141 or 161 or 171 suggested.**Last Offered: Fall 2019* - MTH 218 INTRODUCTION TO MATHEMATICAL MODELS IN LIFE SCIENCE
This course is aimed at building problem-solving ability in students through the development of mathematical models for certain real-life situations in the biological sciences. Models treated cover a variety of phenomena both discrete and continuous, linear and non-linear, deterministic and stochastic. Some topics that might be treated are Leslie Matrices in Demographics, Exponential and Logistic growth, Gompertz growth in tumors, Hardy-Weinberg Law in population genetics, Lotka-Volterra predator-prey systems, principle of competitive exclusion, the Kermack-McKendrick model of epidemics (and variants), Markov chain models (with the requisite intro to probability) and the stochastic pure birth process and epidemic models.

*Prerequisites: MTH 143, 162 or 172. MTH 218 is a required course for the epidemiology major but is not a prerequisite or co-requisite for anything in math.**Last Offered: Spring 2019* - MTH 230 NUMBER THEORY WITH APPLICATIONS
Divisibility, primes, congruences, quadratic residues and quadratic reciprocity, primitive roots, and selected topics, with applications to cryptography and computer science.

*Prerequisites: MTH 172 or MTH 200W or MTH 235.**Last Offered: Fall 2019* - MTH 233 INTRODUCTION TO CRYPTOGRAPHY
A mathematically-oriented inroduction to modern cryptography: weaknesses of historical cryptosystems, modular arithmetic, primality testing and factorization algorithms, private-key/symmetric cryptosystems, public-key/asymmetric cryptosystems and key-sharing (including RSA and Diffie-Hellman). Additional topics may include zero-knowledge protocols, digital signatures, homomorphic encryption and secured computation, elliptic curve cryptography, lattice-based cryptography, and other applications such as digital voting and cryptocurrencies.

*Prerequisites: Some mathematical sophistication required. MTH 162 or 171 or 230 recommended.**Last Offered: Spring 2019* - MTH 235 LINEAR ALGEBRA
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.

*Prerequisites: MTH 165. MTH 200W recommended.**Last Offered: Fall 2019* - MTH 236 INTRODUCTION TO ALGEBRA I
Basic algebraic structures, including groups, rings, and fields with applications to specific examples.

*Prerequisites: MTH 235 or 173.**Last Offered: Spring 2019* - MTH 236H INTRODUCTION TO ALGEBRA I (HONORS)
Honors version of MTH 236.

*Prerequisites: MTH 235 or 173.**Last Offered: Spring 2019* - MTH 237 INTRODUCTION TO ALGEBRA II
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".

*Prerequisites: MTH 236 or 236H.**Last Offered: Fall 2019* - MTH 238 COMBINATORIAL MATH.
Permutations and combinations; enumeration through recursions and generating functions; Polya's theory of counting; finite geometrics and block designs; counting in graphs.

*Prerequisites: MTH 200 or 235 or 171.**Last Offered: Fall 2019* - MTH 240 INTRODUCTION TO TOPOLOGY
Review of set theory; metric spaces and topological spaces; functions and continuous functions; convergence, completeness, connectedness, and compactness; applications to surfaces.

*Prerequisites: MTH 173 or (MTH 164 and MTH 235) or (MTH 164 and MTH 200).**Last Offered: Spring 2019* - MTH 240H INTRODUCTION TO TOPOLOGY (HONORS)
Honors version of MTH 240.

*Prerequisites: MTH 173 or (MTH 164 and MTH 235) or (MTH 164 and MTH 200).**Last Offered: Spring 2019* - MTH 246 LOGIC AND SET THEORY
Either mathematical logic (propositional calculus; the decision problem; consistency and completeness) or set theory (sets, relations, and mappings; cardinals and ordinals; axiom of choice and equivalents), depending on the year.

*Prerequisites: MTH 200 or 235 or 171.**Last Offered: Fall 2017* - MTH 248 THEORY OF GRAPHS
Paths, circuits, trees; bipartite graphs, matching problems; unicursal graphs, Hamiltonian circuits, factors; independent paths and sets; matrix representations; planar graphs; coloring problems.

*Prerequisites: MTH 173 or MTH 235 or (MTH 200 and MTH 165).**Last Offered: Spring 2019* - MTH 250 INTRODUCTION TO GEOMETRY
Foundations of geometry; isometry, similarity, inversions; introductions to affine, projective, and non-Euclidean geometries.

*Prerequisites: MTH 165 and 200, or 235, or 173. MTH 250 is offered in spring semesters, even years.**Last Offered: Spring 2018* - MTH 255 DIFFERENTIAL GEOMETRY
Torsion, curvature; curves and surfaces in 3-space.

*Prerequisites: MTH 164 and 235, or MTH 174.**Last Offered: Fall 2019* - MTH 263 ORDINARY DIFFERENTIAL EQUATIONS
Theoretical approach to ordinary differential equations and the qualitative behavior of their solutions.

*Prerequisites: MTH 165 or 173.**Last Offered: Spring 2019* - MTH 265 FUNCTIONS OF A REAL VARIABLE I
Real number system, continuity and uniform continuity, mean value theorems, bounded variation, Riemann-Stieltjes integral, sequences of functions.

*Prerequisites: MTH 164 and MTH 235, or MTH 164 and MTH 200, or MTH 174**Last Offered: Fall 2019* - MTH 265H FUNCTIONS OF A REAL VARIABLE I (HONORS)
Honors version of MTH 265.

*Prerequisites: MTH164 and MTH235, or MTH164 and MTH200, or MTH174**Last Offered: Fall 2019* - MTH 266 TOPICS IN REAL ANALYSIS
Continuation of MTH 265/265H. Possible topics: a rigorous exposition of Fourier analysis; multivariable analysis; elementary theory of Hilbert and Banach spaces.

*Prerequisites: MTH 265 or 265H.**Last Offered: Spring 2019* - MTH 270 TOPICS IN DATA SCIENCE
*No description**Last Offered: Spring 2016* - MTH 280 INTRODUCTION TO NUMERICAL ANALYSIS
The numerical solution to mathematical problems by computer: linear systems, approximation, integration, and differential equations; floating point arithmetic and consequent pitfalls of computation.

*Prerequisites: MTH 235 or MTH 173.**Last Offered: Fall 2019* - MTH 281 INTRODUCTION TO FOURIER SERIES, ORTHOGONAL POLYNOMIALS, and BOUNDARY VALUE PROBLEMS
Fourier series and convergence theorems; orthogonal polynomials; applications to some partial differential equations; Fourier transforms.

*Prerequisites: MTH 164 and 165, or MTH 174.**Last Offered: Fall 2019* - MTH 282 INTRODUCTION TO COMPLEX VARIABLES WITH APPLICATIONS
Complex differentiation and integration, analytic functions, singularities, residues, poles, power series, conformal mapping, with some applications. This course is independent of MTH 281.

*Prerequisites: MTH 164 or MTH 174 (MTH 200 or MTH 235 recommended unless you have taken MTH 174).**Last Offered: Spring 2019* - MTH 285 METHODS OF APPLIED MATHEMATICS
Topics emphasized can vary year-to-year. Typical topics covered are: Minimum principles; eigenvalues and dynamical systems; constraints and Lagrange multipliers; differential equations of equilibrium; calculus of variations; stability and chaos; nonlinear conservation laws.

*Prerequisites: MTH 164 and 165, or MTH 174.**Last Offered: Spring 2019* - MTH 287 MATH METHODS IN OPT &PHYSICS
This course introduces techniques in mathematical study of optical phenomena. Emphasis is places on gaining insight and experience in the use of these powerful and elegant tools for describing, solving and resolving optical systems and schema.

*Prerequisites: MTH 164 and MTH 281**Last Offered: Spring 2019* - MTH 300W HISTORY OF MATHEMATICS I
The nature and style of mathematics in ancient Babylonia, Egypt, and Greece; medieval and Renaissance Europe; seventeenth-century Europe; and some aspects of the development of abstraction and rigor in analysis and set theory since 1700. This course has a limited number of seats. Students that need an upper-level writing course in mathematics can explore the alternatives of MTH 200W or MTH 391W. See the Math Department website for more information.

*Prerequisites: Some mathematical sophistication required. MTH 161 or equivalent recommended.**Last Offered: Spring 2019*