Number, Magnitude, Form – The development of the concepts of number, magnitude, and form in mathematics. Topics include the natural numbers, the real numbers, and transfinite numbers, length, area, volume, dimension, and fractals, and knots. Emphasis is on the understanding of ideas and the ability to express them through mathematical arguments

Finite Mathematics – Application of quantitative tools as an aid to problem solving in a variety of areas. Topics include solution techniques for systems of linear equations and inequalities, basic principles of probability and statistics, elementary finance, Markov chains, matrices, and more.

Functions – A survey of the fundamental mathematical functions and their applications including the linear, absolute value, polynomial, rational, exponential, logarithmic, and trigonometric functions.

Calculus I – Differential and elementary integral calculus of functions of one variable. Topics include limits, continuity, derivatives, linear approximation, the Fundamental Theorem of Calculus, and elementary techniques of integration. MATH 150 or placement required.

History of Mathematics – The history of mathematics from its origins to the present with an emphasis on significant problems and their solutions. MATH 151 or permission of instructor required.

Statistics – Introduction to statistical inference. Basic probability, descriptive statistics, sampling distributions, parameter estimation, tests of hypotheses, chi-square tests, regression analysis, analysis of variance, and nonparametric tests. MATH 150 required. Crosslisted with ECON 303.

Calculus II – Continuation and extension of Calculus I. Topics include more advanced integration techniques, limits and improper integrals, vector-valued functions of a single variable, scalar-valued functions of N variables, partial derivatives, geometric volumes, sequences and series. MATH 151 required.

Vector Calculus – Calculus of functions in several variables. Topics include the geometry of Euclidean space, vector algebra, forms, matrices, vector-valued functions, the inverse and implicit function theorems, line and surface integrals, differential forms, and the theorems of Green, Gauss, and Stokes. Applications to physics. MATH 250 required.

Ordinary Differential Equations – An introduction to the theory of ordinary differential equations with an emphasis on methods of solution. Topics include first-order equations, existence and uniqueness, linear equations, equations with constant coefficients, variation of parameters, Laplace transforms, series solutions, systems of equations, numerical methods. MATH 250 required.

Scientific Programming – An introduction to programming via the solution of various problems in mathematics and the sciences. Problem description, development of a model, creation and implementation of a computational method of solution, and assessment of results. MATH 150 required.

Algebraic Structures – An introduction to abstract algebra. Topics include groups, subgroups, quotient groups, homomorphisms, rings, ideals, and fields. Emphasis on constructing, writing, and presenting proofs.
MATH 251 required.

Linear Structures – A study of abstract linear algebra. Topics include vector spaces, linear transformations, matrices, eigenvalues, canonical forms, inner product spaces, and modules. MATH 310 required.

Number Theory – A study of the basic properties of the integers including divisibility, primes and their distribution, unique factorization, the Euclidean algorithm, congruences, primitive roots, arithmetic functions, quadratic reciprocity, Diophantine equations, and other topics. MATH 310 required.

Probability – An introduction to probability theory. Topics include sample spaces, discrete and continuous random variables, density functions, moment generating functions, probability distributions, and the Central Limit Theorem. MATH 250 required.

Real Analysis – A rigorous study of the theoretical structure of calculus including the real numbers, metric spaces, limits, continuity, differentiation, integration, the Fundamental Theorem of Calculus, infinite series, and power series. MATH 310 required.

Complex Analysis – An introduction to the study of functions of a complex variable. Topics include the complex numbers, analytic functions, the elementary functions, complex integration, Taylor and Laurent series, residues, conformal mapping, and applications. MATH 251 required.

Partial Differential Equations – An introduction to second-order partial differential equations in two variables. Topics include wave motion and Fourier series, heat flow and the Fourier integral, Laplace's equation and complex variables, second-order equations in more than two variables, spherical harmonics, and associated special functions of mathematical physics. MATH 252 required.

Differential Geometry – A classical treatment of the differential geometry of curves and surfaces in three-dimensional space. Topics include: Frenet frames, the local theory of parameterized curves, regular surfaces, tangent planes, first and second fundamental forms, the Gauss map, parallel transport and the Gauss-Bonnet Theorem. MATH 251 required.

Knot Theory – The geometry and topology of knots, links, surfaces, and three-dimensional manifolds. Topics include: Continuity, topological equivalence, isotopy, Reidemeister moves, colorings, Alexander and Jones polynomials, Euler characteristic, the classification of surfaces, polyhedral solids and Heegard splittings. MATH 310 or permission of the instructor required.

Senior Seminar – Student presentations of selected mathematical problems and directed readings. Senior status required.

Undergraduate Research – Student-Faculty collaboration on research projects of mutual interest. Permission of the department required.

College Physics I (with lab) – Mechanics is foundational to physics. Topics include: rectilinear and rotational motions of particles and rigid bodies, forces, energy methods, conservation laws, and oscillations and waves. MATH 150 required.

College Physics II (with lab) – Thermodynamics, electricity and magnetism, and optics are essential aspects of classical physics. Topics include: temperature, heat and its transfer, the Laws of Thermodynamics, electric force, field, potential and current, capacitance, resistance, induction, circuits, and optics. MATH 150 required.

University Physics I (with lab) – Mechanics is foundational to the study of physics.  Topics include: rectilinear and rotational motions of particles and rigid bodies, forces, energy methods, conservation laws, and Newton’s Law of Universal Gravitation. MATH 151 required.

University Physics II (with lab) – Oscillatory and wave-like behavior are ubiquitous in nature. The production and flow of thermal energy -- heat -- are governed by the Laws of Thermodynamics.  Topics include: materials, oscillations, waves, interference and diffraction, geometric optics, and the Laws of Thermodynamics.  PHYS 221 required.

University Physics III – Maxwell’s unification of electricity and magnetism was a revolutionary development in classical physics. Topics include: electric force, field, potential and current, capacitance, resistance, magnetism, induction, AC/DC circuits, and Maxwell’s Equations along with their vacuum solutions.  PHYS 221 and MATH 250 required.

Intermediate Mechanics – Topics include: central force potentials, Lagrangian and Hamiltonian formulations of dynamics, fluids. PHYS 323 required.

Thermodynamics and Statistical Mechanics – Topics include: classical formulation of Thermodynamic Laws; Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac distributions and applications. PHYS 323 required.

Electricity and Magnetism I – Topics include: Maxwell’s equations in differential form, electrodynamics, electromagnetic waves, special relativity. PHYS 323 required.

Quantum Mechanics I – Topics include: quantum operators, one-dimensional wells and barriers, Born interpretation, Schroedinger equation, Uncertainty Principle, central force problems, angular momentum, spin, addition of angular momenta. PHYS 323 or permission of instructor required.

Quantum Mechanics II – Topics include: fermions and bosons, perturbation theory (time independent and time dependent), variational methods, WKB approximation, scattering. PHYS 361 required.