# Mathematics Degree Requirements

## 2018 - 2019 Catalog

The Mathematics department has the following degrees:

## Mathematics major leading to BA degree

A **major in mathematics** leading to a Bachelor of Arts degree requires the completion of at least 33 credits as follows:

- MATH 221, 222, 311, 312, 321, 322
- One course selected from BIOL 274, 282; CHEM 260, 261; CSCI 211, 313; ECON 302, 320; ENGN 203; GEOL 250; MATH 270, 310, 333, 353; PHYS 112
- 12 additional credits selected from mathematics courses numbered above 300.

Additional courses required as prerequisites for completion of the above include MATH 101 and 102, or their equivalents; furthermore, the course selected to fulfill requirement 2 above may have prerequisites.

- Required courses:
- MATH 221 - Multivariable Calculus
FDR SC Credits 3 Prerequisite The equivalent of MATH 102 with C grade or better. Note: Students needing this course to fulfill an FDR requirement should add to a waiting list when open; additional sections may be added Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

- MATH 222 - Linear Algebra
Credits 3 Prerequisite MATH 221 Introductory linear algebra: systems of linear equations, matrices and determinants, vector spaces over the reals, linear transformations, eigenvectors, and vector geometry.

- MATH 311 - Real Analysis I
Credits 3 Prerequisite MATH 221 with C grade or better; MATH 301 is recommended Basic properties of real numbers, elementary topology of the real line and Euclidean spaces, and continuity and differentiability of real-valued functions on Euclidean spaces.

- MATH 312 - Real Analysis II
Credits 3 Prerequisite MATH 311 Riemann integration, nature and consequences of various types of convergence of sequences and series of functions, some special series, and related topics.

- MATH 321 - Abstract Algebra I
Credits 3 Prerequisite MATH 222; MATH 301 is recommended Groups, including normal subgroups, quotient groups, permutation groups. Cauchy's theorem and Sylow's theorems.

- MATH 322 - Abstract Algebra II
Credits 3 Prerequisite MATH 321 Rings, including ideals, quotient rings, Euclidean rings, polynomial rings. Fields of quotients of an integral domain. Further field theory as time permits.

- One course selected from:
- BIOL 274 - Structural Biology
Credits 4 Prerequisite BIOL 111 and 113, MATH 102 (or equivalent), and CHEM 112 or instructor consent. Faculty Staff This course covers: (a) the fundamental concepts of structural biology (chemical building blocks, structure, superstructure, folding. etc.); (b) software for visualization, visualization styles, publication quality images; (c) the hierarchical nature of biomacromolecular structure classification; (d) computational methods to evaluate and compare biomacromolecular structure; (e) inferring structure/function relationships from structure; and (f) computational prediction of protein structure from sequence. Laboratory course.

- BIOL 282 - Problem Solving in Biological Systems: A Modeling Approach
FDR SL Credits 4 Prerequisite MATH 101 Faculty Toporikova Biological systems are incredibly complex and include multiple interactions, which makes them hard to understand and to predict the outcomes. In this course, students learn how to solve complex problems inspired by biological systems

using a modeling approach. Students learn to identify most essential elements of biological systems, construct the

verbal and graphical models, translate them to a computational software, and make predictions that are relevant for

health policy, conservation efforts, or experimental outcomes. The topics include spread of infectious diseases,

population dynamics, physiology, and neuroscience. Laboratory course. - CHEM 261 - Physical Chemistry: Quantum & Computational Chemistry
Credits 3 Prerequisite CHEM 110 and MATH 102 and junior standing Faculty Tuchler An introduction to quantum mechanics as it applies to atomic and molecular systems. The emphasis is placed on spectroscopic methods and the modern picture of chemical bonding and molecular structure. The accompanying lab focuses on computational methods to illustrate course topics. Laboratory course.

- CSCI 211 - Algorithm Design and Analysis
Credits 3 Prerequisite CSCI 112 and MATH 121 or MATH 301 Faculty Staff Methods for designing efficient algorithms, including divide-and-conquer, dynamic programming, and greedy algorithms. Analysis of algorithms for correctness and estimating running time and space requirements. Topics include advanced data structures, graph theory, network flow, and computational intractability.

- CSCI 313 - Theory of Computation
Credits 3 Prerequisite MATH 121 or MATH 301 or instructor consent Faculty Levy A study of the principles of computer science embodied in formal languages, automata, computability, and computational complexity. Topics include context-free grammars, Turing machines, and the halting problem.

- ECON 302 - Game Theory
Credits 3 Prerequisite MATH 101 or equivalent and ECON 210 Faculty Guse This course abandons the assumptions of perfect competition. Buyers and sellers may be few; information may be privately held; property rights may poorly enforced; externalities abound and uncertainty is the rule. Game theory is a general framework for analyzing the messy world of strategic interactions. Standard solution concepts such as Nash Equilibrium, subgame perfection, and Bayesian equilibrium are introduced in the context of a broad array of microeconomic topics. These include auctions, bargaining, oligopoly, labor market signaling, public finance and insurance. Class time combines lectures, problem-solving workshops, and classroom experiments.

- ECON 320 - Mathematical Economics
Credits 3 Prerequisite ECON 100 or both 101 and 102; and MATH 221. Preference to ECON majors during the first round of registration. Other majors are encouraged to add to the waiting list after registration re-opens for all class years Faculty Grajzl An introduction to fundamental mathematical methods of economic analysis with a variety of applications from both microeconomics and macroeconomics. Topics covered include theory and applications of linear algebra, multivariable calculus, static optimization, and comparative statics. The course is highly recommended for anyone planning to undertake graduate studies in economics or a closely related field.

*Should not be taken if completed ECON 220: Mathematical Economics.* - ENGN 203 - Mechanics I: Statics
Credits 3 Prerequisite Grade of C or better in MATH-101 and PHYS-111 (PHYS 111 as corequisite with instructor consent) Faculty D'Alessandro The science of mechanics is used to study bodies in equilibrium under the action of external forces. Emphasis is on problem solving: trusses, frames and machines, centroids, area moments of inertia, beams, cables, and friction.

- GEOL 250 - Structural Geology and Tectonics
Credits 4 Prerequisite MATH 101 and GEOL 100 or GEOL 101 Faculty Connors Description and methods of analysis of large- and small-scale structural features of the Earth's crust. Topics also include the analysis of geometry, strain and stress as they relate to deformation in the earth. Rock mechanics, application of structural geology in environmental engineering and resource exploration, geometric and computational techniques used in structural analysis, interpretation of geologic maps, and the structural development of mountain systems are also covered. Laboratory course.

- MATH 270 - Financial and Actuarial Mathematics
Credits 3 Prerequisite MATH 102 Faculty Staff Topics include the time value of money, the force of interest, annuities, yield rates, amortization schedules, bonds, contracts, options, swaps, and arbitrage. Equal emphasis is given to both the theoretical background and to the computational aspects of interest theory. This course helps prepare students for the Financial Mathematics actuary exam.

- MATH 310 - Mathematical Statistics
Credits 3 Prerequisite MATH 309 Sampling distributions, point and interval estimation, testing hypotheses, regression and correlation, and analysis of variance.

- MATH 333 - Partial Differential Equations
Credits 3 Prerequisite MATH 332 An introduction to the study of boundary value problems and partial differential equations. Topics include modeling heat and wave phenomena, Fourier series, separation of variables, and Bessel functions. Techniques employed are analytic, qualitative, and numerical.

- MATH 353 - Numerical Analysis
Credits 4 Prerequisite MATH 221 and 222 Faculty Siehler Analysis, implementation, and applications of algorithms for solving equations, fitting curves, and numerical differentiation and integration. Theorems and proofs are complemented by hands-on programming exercises fostering a concrete understanding of accuracy, efficiency and stability, as well as an awareness of potential pitfalls in machine arithmetic. No previous programming experience is required.

- PHYS 112 - General Physics II
FDR SL Credits 3 Prerequisite PHYS 111. Corequisite: PHYS 114 Faculty Staff A continuation of PHYS 111. Topics include electricity and magnetism, optics, relativity, and quantum theory. This course must be taken simultaneously with PHYS 114.

- 12 additional credits selected from mathematics courses numbered above 300.

## Mathematics major leading to BS degree

A **major in mathematics** leading to a Bachelor of Science degree requires the completion of at least 51 credits as follows:

- MATH 221, 222, 311, 312, 321, 322; PHYS 111, 112, 113, 114
- CSCI 111 or 121
- 15 additional credits selected from mathematics courses numbered above 300
- Six additional credits selected from courses in biology, chemistry, computer science, engineering, geology, mathematics (numbered 200 and above), and physics, except courses excluded from degree programs in those subjects.

Additional courses required as prerequisites for completion of the above include MATH 101 and 102 or their equivalents.

- Required courses:
- MATH 221 - Multivariable Calculus
FDR SC Credits 3 Prerequisite The equivalent of MATH 102 with C grade or better. Note: Students needing this course to fulfill an FDR requirement should add to a waiting list when open; additional sections may be added Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green's Theorem.

- MATH 222 - Linear Algebra
Credits 3 Prerequisite MATH 221 Introductory linear algebra: systems of linear equations, matrices and determinants, vector spaces over the reals, linear transformations, eigenvectors, and vector geometry.

- MATH 311 - Real Analysis I
Credits 3 Prerequisite MATH 221 with C grade or better; MATH 301 is recommended Basic properties of real numbers, elementary topology of the real line and Euclidean spaces, and continuity and differentiability of real-valued functions on Euclidean spaces.

- MATH 312 - Real Analysis II
Credits 3 Prerequisite MATH 311 Riemann integration, nature and consequences of various types of convergence of sequences and series of functions, some special series, and related topics.

- MATH 321 - Abstract Algebra I
Credits 3 Prerequisite MATH 222; MATH 301 is recommended Groups, including normal subgroups, quotient groups, permutation groups. Cauchy's theorem and Sylow's theorems.

- MATH 322 - Abstract Algebra II
Credits 3 Prerequisite MATH 321 Rings, including ideals, quotient rings, Euclidean rings, polynomial rings. Fields of quotients of an integral domain. Further field theory as time permits.

- PHYS 111 - General Physics I
FDR SL Credits 3 Prerequisite or corequisite: MATH 101 or equivalent. Corequisite: PHYS 113 Faculty Staff An introduction to classical mechanics and thermodynamics. Topics include Newton's laws, wave motion, and the laws of thermodynamics. This course must be taken simultaneously with Physics 113.

- PHYS 112 - General Physics II
FDR SL Credits 3 Prerequisite PHYS 111. Corequisite: PHYS 114 Faculty Staff A continuation of PHYS 111. Topics include electricity and magnetism, optics, relativity, and quantum theory. This course must be taken simultaneously with PHYS 114.

- PHYS 113 - General Physics Laboratory I
FDR SL Credits 1 Prerequisite Corequisite: PHYS 111. A laboratory course to accompany PHYS 111 Faculty Staff Laboratory exercises in classical mechanics. Laboratory course with fee.

- PHYS 114 - General Physics Laboratory II
FDR SL Credits 1 Prerequisite Corequisite: PHYS 112. A laboratory course to accompany PHYS 112 Faculty Staff Laboratory exercises in electricity and magnetism, optics, and modern physics. Laboratory course with fee.

- Take one of the following courses:
- CSCI 111 - Fundamentals of Programming I
FDR FM Credits 4 Faculty Staff A disciplined approach to programming with Python. Emphasis is on problem-solving methods, algorithm development, and object-oriented concepts. Lectures and formal laboratories.

- CSCI 121 - Scientific Computing
FDR FM Credits 4 Faculty Levy An introduction to computer programming for scientific applications and a survey of the main methodological areas of scientific computation. The course provides the tools needed for students to use computers effectively in scientific work, whether in physics, chemistry, mathematics, economics, biology, psychology, or any field involving quantitative work. Programming in Matlab, a scientific-computing software package, with a focus on topics relevant to students' major fields of study. Lectures and formal labs.

- 15 additional credits selected from mathematics courses numbered above 300
- Six additional credits selected from courses in

biology, chemistry, computer science, engineering, geology, mathematics (numbered 200 and above), and physics, except courses excluded from degree programs in those subjects.