# Mathematics Degree Requirements

## 2015 - 2016 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; CHEM 260, 261; CSCI 211, 313; ECON 220, 301; 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

Planned Offering: Fall, Winter*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

Planned Offering: Fall, Winter*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

Planned Offering: Fall*Prerequisites: 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

Planned Offering: Winter*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

Planned Offering: Fall*Prerequisites: 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

Planned Offering: Winter*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

Planned Offering: No scheduled years*Prerequisite: BIOL 111 and 113, MATH 102 (or equivalent), and CHEM 112 or instructor consent.*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.

- CHEM 261 - Physical Chemistry: Quantum & Computational Chemistry
Credits: 3

Planned Offering: Fall, 2014*Prerequisites: CHEM 110 and MATH 102 and junior standing.*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

Planned Offering: Winter*Prerequisites: CSCI 112 and MATH 121 or MATH 301.*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

Planned Offering: Winter*Prerequisites: MATH 121 or MATH 301 or instructor consent.*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 220 - Mathematical Economics
Credits: 3

Planned Offering: Fall or Winter*Prerequisites: ECON 101, 102, and MATH 221.*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.

- ENGN 203 - Mechanics I: Statics
Credits: 3

Planned Offering: Fall*Prerequisite: MATH-102, PHYS-111 (PHYS 111 as corequisite with instructor consent)*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

Planned Offering: Winter 2016 and alternate years*Prerequisite: MATH 101 and GEOL 100, GEOL 101 or GEOL 105.*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

Planned Offering: Winter 2014 and alternate years*Prerequisite: MATH 102.*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 II
Credits: 3

Planned Offering: Winter 2016 and alternate years*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

Planned Offering: Winter*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

Planned Offering: Spring 2015 and alternate years*Prerequisites: MATH 221 and 222.*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

Planned Offering: Winter*Prerequisite: PHYS 111.**Corequisite: PHYS 114*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

Planned Offering: Fall, Winter*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

Planned Offering: Fall, Winter*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

Planned Offering: Fall*Prerequisites: 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

Planned Offering: Winter*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

Planned Offering: Fall*Prerequisites: 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

Planned Offering: Winter*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

Planned Offering: Fall*Prerequisite or corequisite: MATH 101 or equivalent.**Corequisite: PHYS 113*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

Planned Offering: Winter*Prerequisite: PHYS 111.**Corequisite: PHYS 114*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

Planned Offering: Fall*Corequisite: PHYS 111. A laboratory course to accompany PHYS 111.*Laboratory exercises in classical mechanics.

- PHYS 114 - General Physics Laboratory II
FDR: SL

Credits: 1

Planned Offering: Winter*Corequisite: PHYS 112. A laboratory course to accompany PHYS 112.*Laboratory exercises in electricity and magnetism, optics, and modern physics.

- Take one of the following courses:
- CSCI 111 - Fundamentals of Programming I
FDR: FM

Credits: 4

Planned Offering: Fall, WinterA 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

Planned Offering: WinterAn 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.