# Mathematics (MAT) Courses

**MAT-003 Pre-Calculus**

This course is intended solely for those students
who wish to take calculus, but whose preparaton
makes a refresher course in pre-calculus
advisable. Topics covered include a review of
algebra (solving equations and inequalities,
simplification of algebraic expressions) and
properties of elementary functions (polynomial,
rational, exponential, logarithmic, and
trigonometric functions) with special emphasis on
graphing these functions. MAT 003 cannot be used
for any distribution credit or any area of
concentration. (For students who desire a
distribution credit in mathematics but do not
wish to take calculus, MAT-103, MAT-104, MAT-106,
and MAT-108 are recommended.)** Prerequisites:** none**Credits: **0.5

**MAT-010 Pre-Calc With Intro to Calculus**

This course is intended solely for those students
whose intended course of study requires calculus,
but whose preparation makes a slower-paced course
in calculus advisable. The course combines a
review of pre-calculus with the beginning of an
introduction to calculus. Topics include solving
equations and inequalities, simplification of
algebraic expressions, polynomials, rational
functions, exponential functions, trigonometric
functions, limits, continuity, the definition of
the derivative and its geometric interpretation,
and basic differentiation rules. The focus is on
understanding basic concepts and gaining basic
computational skills. This course cannot be used
for any distribution credit nor any area of
concentration. (We recommend MAT 103, 104, 106, or
108 for students who desire a distribution credit
in mathematics but do not need calculus for their
major or minor.)** Prerequisites:** none**Corequisites:** MAT-010 placement**Credit: **1

**MAT-100 Math Modeling and Precalculus**

This course develops problem solving skills
fundamental to further study in higher mathematics
through mathematical modeling and applications.
Students will study algebraic and graphical
properties of polynomial, rational, exponential,
logarithmic, and trigonometric functions, with a
focus on using these to build and understand
mathematical models. With a dual emphasis on
sharpening core skills and understanding
applications, this course provides a review of
material relevant for continuing to a full course
in calculus. This course is limited to students
who intend to continue to MAT-111 as a requirement
for his major, but whose placement indicates that
a precalculus course is advisable. While it
satisfies the Quantitative Literacy (QL)
distribution requirement, enrollment in MAT 100 is
only available through instructor permission. For
students who need distribution credit in QL but do
not require a subsequent course in calculus,
MAT-103, MAT-104, MAT-106, and MAT-108 are
recommended. MAT-100 does not count toward a major
or minor in mathematics.** Prerequisites:** none**Corequisites:** MAT-100 placement and instructor permission**Credit: **1

** Distribution:** Quantitative Literacy

**MAT-103 Probability**

The course introduces students to key measures of
uncertainty (probability) and long-run average
(expected value). Probabilistic reasoning is
applied to a wide variety of interesting in the
areas of medical testing, gambling, game theory,
sports, asset-price modelling, financial
derivatives, insurance, and retirement annuities.
MAT-103 does not count toward the mathematics
major or minor. Credit cannot be given for both
MAT-103 and MAT-253. The course is offered most
semesters.** Prerequisites:** none**Credits: **0.5

** Distribution:** Quantitative Literacy

**MAT-104 Statistics**

The course looks briefly at some standard
statistics: averages, variances, standard
deviations, medians, and proportions. Correlation
coefficients are introduced and used for
prediction. The classical p-value approach to
claim testing is presented and applied to a wide
variety of testing situations. In addition, the
classical confidence interval approach to
estimation is examined. MAT-104 does not count
toward the mathematics major or minor. (MAT-103 is
not a prerequisite for MAT-104). Credit cannot be
given for both MAT-104 and MAT-254. The course is
offered most semesters.** Prerequisites:** none**Credits: **0.5

** Distribution:** Quantitative Literacy

**MAT-106 Topics in Contemporary Math**

A study of selected topics dealing with the nature
of mathematical ideas. This course focuses on
mathematics as a creative endeavor. Through
participation and discovery, students will
consider an articulation of mathematics that
focuses on patterns, abstraction, and inquiry.
Topics will vary, but could include logic,
Euclidean geometry, algorithms, etc. This course
does not count toward the major or minor in
mathematics. Refer to the Course Descriptions
document on the Registrar's webpage for topics and
descriptions of current offerings.** Prerequisites:** none**Credit: **1

** Distribution:** Quantitative Literacy

**MAT-108 Intro to Discrete Structures**

An introduction to discrete mathematics for
students not planning to major in mathematics.
Topics include sets and logic, proof methods,
counting arguments, recurrence relations, graphs,
and trees. This course may be used to meet the
mathematics requirement for the computer science
minor. However, it does not count toward the
mathematics major or minor. Students may not
present both MAT 108 and 219 for credit toward
graduation.** Prerequisites:** none**Credit: **1

** Distribution:** Quantitative Literacy

**MAT-110 Calc I With Pre-Calc Review**

This course is intended solely for those students
who took and passed MAT-010 and students whose
intended course of study requires calculus.
Successful completion of this course is equivalent
to completion of MAT-111. Topics covered include
implicit differentiation, the graphical behavior
of the derivative, applications of the derivative,
an introduction to integration, the Fundamental
Theorem of Calculus, and integration by
substitution. The focus is on understanding basic
concepts and gaining basic computational skills.
This course counts as a distribution credit in
mathematics. Credit cannot be given for both
MAT-110 and MAT-111.** Prerequisites:** MAT-010 with a grade of C- or better.**Credit: **1

** Distribution:** Quantitative Literacy** Equated Courses:** MAT-111

**MAT-111 Calculus I**

This course studies the fundamentals of
single-variable calculus, developing analytical
and computational skills appropriate for students
in quantitatively rigorous disciplines. Topics
include limits, continuity, techniques of
differentiation, applications of derivatives, the
Mean Value Theorem, the Intermediate Value
Theorem, the Fundamental Theorem of Calculus, and
the method of substitution for integration.** Prerequisites:** MAT-100 with a minimum grade of C-, or MAT-111 placement, or
permission of the instructor**Credit: **1

** Distribution:** Quantitative Literacy** Equated Courses:** MAT-110

**MAT-112 Calculus II**

This course continues the study of calculus from
MAT-111, developing analytical and computational
skills appropriate for students in quantitatively
rigorous disciplines. Topics include techniques
and applications of integration, numerical
integration, improper integrals, infinite
sequences and series, Taylor series, and an
introduction to multivariable calculus including
partial derivatives and multiple integrals.** Prerequisites:** MAT-110 or MAT-111 with a minimum grade of C-,
or MAT-112 placement**Credit: **1

** Distribution:** Quantitative Literacy

**MAT-178 Special Topics**

This course is designed for the treatment of
material outside the regular offerings of the
department. For a given semester, the course
content and other particulars will be announced
before advance registration for that semester.
Refer to the Course Descriptions document on the
Registrar's webpage for topics and descriptions of
current offerings.** Prerequisites:** none**Credits: **0.5-1

** Distribution:** Quantitative Literacy

**MAT-219 Combinatorics**

This course is an introduction to combinatorial
reasoning and discrete mathematics. Topics include
enumeration, combinatorial identities, graph
theory, generating functions, and recurrence
relations. Additional topics may include graph
algorithms, partitions, and partially ordered
sets. Students may not present both MAT 108 and
219 for credit towards graduation. This course is
offered in the spring semester.** Prerequisites:** MAT-223**Credit: **1

**MAT-221 Geometry**

This course studies aspects of the development of
Euclidean and non-Euclidean geometries from a
modern and/or historical viewpoint.** Prerequisites:** MAT-112**Credit: **1

**MAT-222 Number Theory**

A study of elementary number theory. Topics
include divisibility, congruences, properties of
prime numbers, linear Diophantine equations, the
Euler phi function, primitive roots, and
additional topics. Such topics may include public
key cryptography, quadratic reciprocity, and
Pythagorean triples. This course is offered in the
spring semester.** Prerequisites:** MAT-112**Credit: **1

**MAT-223 Linear Algebra**

An introduction to linear equations and vector
spaces. Topics include solving linear equations,
matrix algebra, row operations, determinants,
vector spaces, bases and dimension, linear
transformations, eigenvalues and eigenvectors, and
orthogonality. Optional topics include least
squares problems, matrix factorization, and other
applications. An important aspect of the course is
to introduce the student to abstract thinking and
proofs.** Prerequisites:** MAT-112 with a minimum grade of C-, or MAT-223
placement**Credit: **1

** Distribution:** Quantitative Literacy

**MAT-224 Differential Equations**

An introduction to ordinary differential
equations. Special solution techniques and some
theory for first-order and linear equations
including integrating factors, constant
coefficients, undetermined coefficients, variation
of parameters, power series solutions, Laplace
transforms, and systems of differential equations
with applications. This course is offered in the
spring semester.** Prerequisites:** MAT-112 with a minimum grade of C-, and MAT-223**Credit: **1

**MAT-225 Multivariable Calculus**

This course builds on the introduction to calculus
in higher dimensions in MAT-112. Topics covered
include limits, continuity, differentiability,
directional derivatives, constrained and
unconstrained optimization, geometry of curves,
multiple integrals, general coordinate systems,
path and surface integrals, vector calculus,
theorems of Green and Stokes, and applications.
This course is offered in the fall semester.** Prerequisites:** MAT-112 with a minimum grade of C-, and MAT-223**Credit: **1

** Distribution:** Quantitative Literacy

**MAT-226 Operations Research**

Linear and nonlinear optimization, linear
programming, integer programming, duality,
combinatorics, the simplex method and related
algorithms, game theory, Markov chains, queuing
theory.** Prerequisites:** MAT-223**Credit: **1

**MAT-235 Stochastic Simulation**

Interesting real world phenomena often involve
randomness at some level, and this course
develops mathematical and computational tools for
studying these systems. In particular, students
will study and implement computer simulation
models of continuous and discrete stochastic
processes with potential applications in physics,
economics, epidemiology, networks, sports,
elections, and industrial engineering. Specific
topics for study include: basic probability
models, pseudo-random number generation, queueing
models, discrete event simulations, Poisson
processes, random walks, Markov chains, Monte
Carlo methods, and statistical analysis of
simulated data.** Prerequisites:** MAT-112 and CSC-111**Credit: **1

**MAT-251 Mathematical Finance**

This course gives an overview of the mathematical
reasoning behind the pricing of financial
derivatives. Special emphasis is given to
replication arguments and using risk-neutral
distributions in the binomial pricing model and
using risk neutral distributions in the geometric
Brownian motion model. A probabilistic derivation
of the Black-Scholes pricing formula for gap call
options is given. Other topics covered include
put-call parity, delta hedging, value at risk, and
compound options. The course is typically offered
every fall semester.** Prerequisites:** MAT-112**Credits: **0.5

**MAT-252 Mathematical Interest Theory**

This course gives a thorough treatment of the
mathematical theory of interest, with special
attention paid to calculating present and
accumulation values for annuities (series of
payments made at regular time intervals). Some
topics include nominal and effective rates of
interest and discount, force of interest,
amortization schedules, sinking funds, bonds,
duration, and the use of modified duration to
measure bonds' sensitivity to changes in the yield
rate. This course is typically offered every fall
semester.** Prerequisites:** MAT-112**Credits: **0.5

**MAT-253 Probability Models**

This course is a standard calculus-based
introduction to discrete and continuous random
variables. Discrete distributions considered
include the hypergeometric, binomial, geometric,
Poisson, and discrete uniform. Continuous
distributions considered include the gamma,
chi-square, normal, beta, t and F. The Central
Limit Theorem is covered, as well as multivariate
distributions (including the bivariate normal and
multinomial distributions), and transformations of
random variables. Credit cannot be given for both
MAT-103 and MAT-253. This course is typically
offered in the fall semester.** Prerequisites:** MAT-112**Credits: **0.5

**MAT-254 Statistical Models**

This course gives an overview of confidence
intervals and classical hypothesis testing
procedures: z-tests, t-tests, F-tests, Chi-square
tests, and regression. An intuitive but
mathematical treatment is given for all the
distributions and procedures involved. Credit
cannot be given for both MAT-104 and MAT-254. This
course is typically offered in the spring
semester.** Prerequisites:** MAT-112**Credits: **0.5

**MAT-277 Special Topics**

This course is designed for the treatment of
material outside the regular offerings of the
department. For a given semester, the course
content and other particulars will be announced
before advance registration for that semester.
Refer to the Course Descriptions document on the
Registrar's webpage for topics and descriptions of
current offerings.** Prerequisites:** none**Credit: **1

**MAT-287 Independent Study**

Individual research projects. The manner of study
will be determined by the student in consultation
with the instructor. Students must receive
written approval of their project proposal from a
department Chair before registering for the
course.** Prerequisites:** none**Credits: **0.5-1

**MAT-314 Modeling With Differential Equations**

A course to develop the basic skills of
formulation, simplification, and analysis of
mathematical models for describing and predicting
phenomena in the natural and social sciences,
with special emphasis in modeling with
differential equations. Topics may be taken from
fields such as physics, chemistry, biology,
psychology, economics, and political science.
This course is offered in the fall semester of
even-numbred years.** Prerequisites:** MAT-224**Credit: **1

**MAT-323 Topics in Linear Algebra**

An in-depth study of some of the topics covered
in MAT 223, including the theory of vector
spaces, linear transformations, and Euclidean
spaces, together with some additional topics,
which may include isomorphisms, duality,
canonical forms, and applications of linear
algebra. Refer to the Course Descriptions document
on the Registrar's webpage for topics and
descriptions of current offerings.** Prerequisites:** MAT-223**Credit: **1

**MAT-324 Topics in Differential Equations**

A second course in differential equations
offering study of special topics in more depth or
beyond those covered in MAT 224. Topics may
include existence and uniqueness theory,
stability theory, Green's functions, dynamical
systems, partial differential equations, and
applications of differential equations. Refer to
the Course Descriptions document on the
Registrar's webpage for topics and descriptions of
current offerings.** Prerequisites:** MAT-224**Credit: **1

**MAT-331 Abstract Algebra I**

This course is a first course in algebraic
structures and higher abstract mathematics. The
algebraic structures studied are groups and rings,
which generalize symmetry and familiar number
systems like the integers or real numbers. Topics
include modular arithmetic, subgroups, quotient
groups, isomorphism theorems, and permutation
groups. This course has a strong emphasis placed
on writing and reading mathematical proofs. This
course is offered in the spring semester.** Prerequisites:** MAT-223 with a minimum grade of C-**Credit: **1

**MAT-332 Abstract Algebra II**

This course is a continuation of MAT-331. Topics
will depend on the instructor but may include
fields, modules, Galois theory, algebraic
geometry, Gröbner bases, or advanced topics in
groups and rings. This course has a strong
emphasis placed on writing and reading
mathematical proofs.** Prerequisites:** MAT-331**Credit: **1

**MAT-333 Funct Real Variable I**

A first course in the foundations of modern
analysis. Topics include set theory, topology of
the real numbers, sequences, series,
differentiation, integration, and rigorous proofs
of the major theorems of single-variable
calculus. This course is offered in the fall
semester.** Prerequisites:** MAT-223**Credit: **1

**MAT-334 Funct Real Variable II**

A continuation of MAT 333. Topics will depend on
the instructor but may include sequences and
series of functions, Fourier analysis, elementary
functional analysis, advanced multivariable
calculus or metric spaces.** Prerequisites:** MAT-333**Credit: **1

**MAT-337 Numerical Analysis**

This course provides a broad introduction to the
field of numerical analysis. Topics of study
include rootfinding, numerical linear algebra,
function approximation, numerical differentiation
and integration, and numerical methods for
differential equations. The primary focus
involves the derivation, analysis and
implementation of numerical methods, but the
course also includes discussion of uses and
implications of these methods in applications.
This course is offered in the fall semester of
even-numbered years.** Prerequisites:** CSC-111 and MAT-223**Credit: **1

**MAT-338 Topics Computational Math**

This course develops mathematical and
computational techniques in areas of mathematics
or interdisciplinary study in which computation
plays a central and essential role. Topics vary by
semester but they may include computational
geometry, computer algebra, scientific computing,
and symbolic computation. This course is offered
in the fall Refer to the Course Descriptions
document on the Registrar's webpage for topics and
descriptions of current offerings. semester of
odd-numbered years.** Prerequisites:** CSC-111 and MAT-112**Credit: **1

**MAT-341 Topology**

An introduction to point-set topology. Topics
include topological spaces, continuous functions,
product and quotient spaces, metric spaces,
connectedness, and compactness.** Prerequisites:** MAT-223**Credit: **1

**MAT-344 Complex Analysis**

This course develops the core analytical framework
for complex functions of one variable. Topics
include basic operations and properties of the
complex plane, transformations of elementary
functions, analytic functions, contour integrals,
theory of residues, and conformal mapping. This
course is offered in the spring semester of
odd-numbered years.** Prerequisites:** MAT-223**Credit: **1

**MAT-353 Probability Models II**

This course is a continuation of MAT-253
(Probability Models) with a focus on applications
to financial problems. Brownian motion and Ito
integrals are introduced and used for ruin theory
calculations and applied to some simple investment
models with continuous trading. The compound
Poisson, mixed, and mixture distributions are used
for some insurance settings. Expected present
value and variance of present value are calculated
for a wide variety of life insurance and annuity
problems. The course is typically offered in the
fall semester.** Prerequisites:** MAT-253**Credits: **0.5

**MAT-354 Mathematical Statistics**

This course takes a more theoretical look at
estimation and hypothesis testing than MAT-254
(Statistical Models). Classical estimation topics
include method of moment estimators, maximum
likelihood estimators (MLE's), the information
inequality, and the asymptotic theory of MLE's.
Classical hypothesis testing topics include using
the Neyman-Pearson Lemma to find most powerful
tests and uniformly most powerful tests,
Likelihood ratio tests (LRT's), and the asymptotic
theory of LRT's. The course also looks at the
Bayesian approach to statistical inference, in
particular, the situation with binomial data and
beta priors. This course is typically offered in
the spring semester, loosely alternating with
MAT-355 Regression Models.** Prerequisites:** MAT-253 and MAT-254**Credits: **0.5

**MAT-355 Regression Models**

This course takes a mathematical, matrix-based
look at regression (introduced in MAT-254,
Statistical Models). The probabilistic machinery
needed when working with linear combinations of
normal random variables is developed, including
orthant probability calculation and several
results involving the chi-square distribution. A
general method for hypothesis testing is presented
and used in a variety of testing situations. Time
series models are also looked at and maximum
likelihood estimation in both regression and time
series settings is considered. This course is
typically offered in the spring semester, loosely
alternating with MAT-354 Mathematical Statistics.** Prerequisites:** MAT-223, MAT-253, and MAT-254**Credits: **0.5

**MAT-377 Special Topics**

This course is designed for the treatment of
material outside the regular offerings of the
department. For a given semester, the course
content and other particulars will be announced
before advance registration for that semester.
Refer to the Course Descriptions document on the
Registrar's webpage for topics and descriptions of
current offerings.** Prerequisites:** none**Credits: **0.5-1

**MAT-378 Special Topics**

This course is designed for the treatment of
material outside the regular offerings of the
department. For a given semester, the course
content and other particulars will be announced
before advance registration for that semester.
Refer to the Course Descriptions document on the
Registrar's webpage for topics and descriptions of
current offerings.** Prerequisites:** none**Credits: **0.5-1

**MAT-387 Independent Study**

Individual research projects. The manner of study
will be determined by the student in consultation
with the instructor. Students must receive
written approval of their project proposal from a
department Chair before registering for the
course.** Prerequisites:** none**Credits: **0.5-1

**MAT-388 Independent Study**

Individual research projects. The manner of study
will be determined by the student in consultation
with the instructor. Students must receive
written approval of their project proposal from a
department Chair before registering for the
course.** Prerequisites:** none**Credits: **0.5-1

**MAT-400 Senior Seminar**

Topics in the history and foundations of
mathematics, the special emphasis varying from
year to year. Every student will be expected to
write a term paper. Please refer to the
Registrar's page for course description.** Prerequisites:** none**Credits: **0.5