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Mathematics

Credits:
4
Degree Requirements:
F6

Topics include systems of linear equations, matrices, matrix inversion and applications (including Leontief input-output analysis),
mathematical programming, linear programming and the simplex method, finite Markov chains, and game theory.

Credits:
4
Degree Requirements:
F6

This course is an examination of conventional cryptographic methods (such as substitution and transposition ciphers), public key
methods (such as RSA, a standard method for secure web transactions), and computer-based conventional cryptographic techniques
(block ciphers and hash functions). We will develop and use mathematical tools such as modular arithmetic, probability, matrix algebra,
and number theory both to implement and cryptanalyze these methods. In addition, we will deal with a few of the technical and public
policy issues surrounding uses of encryption.

Credits:
4
Degree Requirements:
F6

A modern introduction to statistical inference. Core topics include one- and two-sample hypothesis testing and confidence interval
construction for means and proportions using both randomization techniques and traditional methods; correlation; and simple linear
regression. Students are introduced to professional statistical packages. Students who have already taken Math 122 should consider
taking Math 311-312 instead. Students who already have credit for Economics 290 may not earn credit for Math 111.

Credits:
4
Degree Requirements:
F6

This one-semester course presents an introduction to applied mathematics and an overview of calculus: applications of the derivative, the definite Integral, the Fundamental Theorem of Calculus, partial derivatives and double integrals. Applications will involve the use of a variety of functions, including exponential, logarithmic and trigonometric functions. Each topic is introduced through the modeling process; computer-based applications and group work are major components of this course. (Note: Students who have already had Math 116 or Math 121 may not earn credit for Math 115. Math 115 is not adequate preparation for Math 122.)

Credits:
4
Degree Requirements:
F6

This course provides a one-semester introduction to the fundamentals of calculus, with applications and examples selected specifically to be of use and interest to students with a major in Commerce and Business, or a career interest in business. Topics include functions and change, the derivative, differentiation techniques, the definite integral, and applications. (Note: Students who have previous credit for Math 121 may not earn credit for Math 116. Students may not earn credit for both Math 115 and Math 116.)

Credits:
4
Degree Requirements:
F6

This course is an introduction to the concepts, formalism, and applications of derivatives and integrals. Elementary transcendental
functions are used throughout; specific topics include limits, the derivative, applications of differentiation, the definite integral, and the Fundamental Theorem of Calculus.

Credits:
4
Degree Requirements:
F6

This course is an introduction to (1) formal and numerical techniques of integration, (2) Taylor’s theorem, sequences, series, power
series, and their applications, (3) applications of integration and series to solving first-order and linear differential equations, and (4)
applications of integration to calculate area, length, volume, probability, work, centroids, and fluid pressure.

Prerequisites:
Credits:
4
Degree Requirements:
F6

A thorough introduction to the reading, writing, presenting and creating of mathematical proofs. Students will learn and practice in a
careful and deliberate way the techniques used to prove mathematical theorems. Proofs studied will be chosen from a variety of fields
such as set theory, number theory, analysis, algebra, and graph theory. Topics also include elements of the history and philosophy of
mathematics and an introduction to the mathematical community.

Prerequisites:
Credits:
4
Degree Requirements:
F6

An introduction to statistics for mathematically inclined students, focusing on learning statistical concepts and inference through investigations. Topics include exploratory graphics, descriptive statistics, sampling methods, bias, observational studies, experimental studies, randomization tests, the binomial, hypergeometric, and normal distributions, significance tests, confidence intervals, normal models, t-procedures, and two-sample procedures.  Students may not earn credit for both Math 111 and Math 211.

Prerequisites:
Credits:
4
Degree Requirements:
F6

This course provides an introduction to a variety of mathematical topics used in analyzing problems arising in the biological sciences, without using calculus.  The mathematics covered in this course all revolve around modeling dynamic biological phenomenon using discrete time steps. Specifically, we will construct and analyze discrete difference equation models, matrix models, and Boolean models.  Some of the biological applications we will explore include modeling the population sizes of various species over time, describing how the concentration of a drug in the body changes over time, modeling the process of ecological succession, modeling the frequency of an allele in a population over generations, and modeling metabolic pathways. In the lab assignments for this course students will learn the fundamentals of programming using the software package Matlab as a means of implementing and analyzing the mathematical models constructed throughout the course. Students are not expected to have prior exposure to computer programming before taking this course.

Credits:
4
Degree Requirements:
F6

A continuation of Math 122: vector calculus, functions of several variables, partial derivatives, multiple integrals, line integrals, and
Green’s theorem.

Prerequisites:
Credits:
4
Degree Requirements:
F6

The theory, methods, and applications of ordinary differential equations. Topics include existence, uniqueness and other properties of
solutions, linear equations, power series and Laplace transform methods, systems of linear equations, and qualitative analysis.

Prerequisites:
Credits:
4
Degree Requirements:
F6

Topics include systems of linear equations, matrix algebra, determinants, real and complex vector spaces, linear transformations,
eigenvalues and eigenvectors, and diagonalization. Attention is given to proofs.

Credits:
4

Topics include the axioms of Kolmogorov, basic combinatorics, conditional probability, independence, various discrete and continuous
probability distributions, expected value, variance, moment-generating functions, characteristic functions, the weak and strong law of
large numbers, the Central Limit Theorem, and simulation. (Course offered in alternate years; scheduled for 2017-2018.)

Co-requisite: MATH 223

Prerequisites:
Credits:
4

This course introduces students to theoretical issues and data-driven applications in statistics. Topics include modes of convergence,
estimation theory, confidence interval construction, hypothesis testing, linear regression, goodness-of-fit tests, and nonparametric tests.
Special emphasis is placed on the use of the Student’s t, F, Z, and chi-squared distributions to draw inferences about the means and
variances of one or two populations. (Course offered in alternate years; scheduled for 2017-2018.)

Prerequisites:
Credits:
4

Agent-based models (ABMs) are algorithms which model the behavior and interaction of individuals (referred to as agents) with each other and their local environment. ABMs have been used to model a diverse array of complex dynamical systems including flocking/swarming/schooling, financial transactions, the growth of a slime mold, and the spread of infectious diseases within a population or network. This class will introduce agent-based modeling and a programming language & environment designed for the implementation of ABMs called NetLogo. After the foundational principles of agent-based modeling are covered, teams of students will identify a system to model, and work to create and implement an ABM to address relevant questions about the behavior of the system being modeled.

Credits:
4
Degree Requirements:
F2i

Mathematical modeling is central to harnessing the power of mathematics in the generation of new scientific knowledge. Students will work in teams to model biological or physical scenarios using systems of differential equations. Students will learn to conduct literature searches, pose and refine research questions, use standard mathematical models, identify which models are applicable to a given research question, modify standard models to novel situations, communicate each of these effectively in writing, and work effectively in a team. A final project will require students to create a polished research article presenting their models. A significant portion of this course will focus on developing fluency in scientific writing.

Prerequisites:
Credits:
4

Topics include the real and complex number systems, metric spaces, sequences and series, continuity, and differentiation, as well as
topics selected from the Riemann and the Riemann-Stieltjes integrals, sequences and series of functions, functions of several real
variables, and Lebesgue theory. Emphasis is on careful proof.

Credits:
4

Topics include the real and complex number systems, metric spaces, sequences and series, continuity, and differentiation, as well as
topics selected from the Riemann and the Riemann-Stieltjes integrals, sequences and series of functions, functions of several real
variables, and Lebesgue theory. Emphasis is on careful proof.

Prerequisites:
Credits:
4

An introduction to the concepts, theory, and basic solution techniques of partial differential equations. Examples studied in detail include
the heat equation, wave equation, and Laplace equation. The theory and applications of Fourier series are introduced. Other topics that
may be covered include numerical methods, modeling, and nonlinear waves. (Course offered in alternate years; scheduled for 2016-
2017.)

Prerequisites:
Credits:
4

An introduction to axiomatic algebraic structures. Topics include groups, subgroups, permutation groups, cyclic groups, normal
subgroups, quotient groups, homomorphisms, isomorphisms, rings, integral domains, polynomial rings, ideals, quotient rings, fields, and
extension fields. Additional topics may include finite fields, Galois theory, and advanced topics from linear algebra. (Course offered in
alternate years; scheduled for 2017-2018.)

Credits:
4

An introduction to axiomatic algebraic structures. Topics include groups, subgroups, permutation groups, cyclic groups, normal
subgroups, quotient groups, homomorphisms, isomorphisms, rings, integral domains, polynomial rings, ideals, quotient rings, fields, and
extension fields. Additional topics may include finite fields, Galois theory, and advanced topics from linear algebra. (Course offered in
alternate years; scheduled for 2017-2018.)

Prerequisites:
Credits:
4

This course is an introduction to the theory of functions of a complex variable. Topics include complex numbers and their properties,
analytic functions and the Cauchy-Riemann equations, complex logarithms, exponential and trigonometric functions, complex
integration and the Cauchy integral formula, complex power series, the residue theorem, and applications to calculations of definite
integrals.

Prerequisites:
Credits:
1

This course will prepare students for the Senior Seminar experience. Students will attend the Senior Seminar presentations, pursue
independent readings, and prepare a Senior Seminar prospectus for approval by the faculty of the department.

Credits:
4

Topics selected from sets, functions, metric spaces, topological spaces, separation properties, compactness, connectedness, the Stone-
Weierstrass theorem, mapping theorems, plane topology.

Credits:
1-4

Qualified students may conduct original research in pure mathematics, applied mathematics, or statistics under the supervision of a
faculty mentor. A student may use four combined credits from 451 and 452 towards one upper-level major elective. Students should
expect to commit at least three hours per week per credit.

Credits:
1-4

Qualified students may conduct original research in pure mathematics, applied mathematics, or statistics under the supervision of a
faculty mentor. A student may use four combined credits from 451 and 452 towards one upper-level major elective. Students should
expect to commit at least three hours per week per credit.

Credits:
1-4

This course allows students to do advanced work not provided for in the regular courses. Its content will be fixed after consultation with
the student and in accord with his or her particular interests.

Credits:
1-4

This course allows students to do advanced work not provided for in the regular courses. Its content will be fixed after consultation with
the student and in accord with his or her particular interests.

Credits:
1-4

Internships in Mathematics, which are normally arranged by the Director of Career Services, permit a qualified student to receive
academic credit for off-campus work experience. Upon completion of the internship, the student makes written and oral reports focusing
on an integration of the student’s academic work and the internship project. Normally the course will be taken on a Pass/Fail basis; it
does not count toward the requirements for the major or minor except with special approval of the department. Interested students should
contact the Chair of the department and the Director of Career Services.

Credits:
4

An occasional offering of topics not covered in the existing mathematics courses. Examples of topics include: graph theory, Fourier
analysis, measure theory, dynamical systems, matrix groups, foundations of mathematics, game theory, set theory, logic, non-Euclidean
geometry, orbifold Euler characteristics, and operations research.

Credits:
4

Topics selected from basic counting principles, Ramsey theory, the inclusion/exclusion principle, recurrence relations, generating
functions, partially ordered sets, systems of distinct representatives, combinatorial designs, graphs, directed graphs, partitions,
combinatorial optimization, enumeration under group action, and an introduction to coding theory. (Course offered every third year;
scheduled for 2014-2015.)

Credits:
2-2, 4-4, or 0-4

Students pursue individual projects supervised by members of the faculty. Seminar sessions focus on issues of effective written and oral
presentation of mathematics. A student may pursue either a research project, in which the student carries out original research on a
suitable topic of interest, or an expository project, demonstrating understanding of mathematics by exploring some topic of established
mathematics which is not covered in a regular course. Students who pursue an expository project may complete the senior seminar
requirement in either one semester (4 credits in the Fall) or two semesters (2 credits in the Fall, 2 credits in the Spring.) Students
pursuing a research project must complete the requirement over two semesters.

Credits:
2-2, 4-4, or 0-4

Students pursue individual projects supervised by members of the faculty. Seminar sessions focus on issues of effective written and oral
presentation of mathematics. A student may pursue either a research project, in which the student carries out original research on a
suitable topic of interest, or an expository project, demonstrating understanding of mathematics by exploring some topic of established
mathematics which is not covered in a regular course. Students who pursue an expository project may complete the senior seminar
requirement in either one semester (4 credits in the Fall) or two semesters (2 credits in the Fall, 2 credits in the Spring.) Students
pursuing a research project must complete the requirement over two semesters.

Credits:
4

The Honors Tutorial provides an alternative to the Senior Seminar for qualified students who wish to pursue an original research project
in greater depth than would be possible otherwise. Criteria for successful completion of an Honors project include originality,
mathematical maturity, progress, and independence.

Credits:
4

The Honors Tutorial provides an alternative to the Senior Seminar for qualified students who wish to pursue an original research project
in greater depth than would be possible otherwise. Criteria for successful completion of an Honors project include originality,
mathematical maturity, progress, and independence.