MT 004 Finite Probability and Applications (Fall/Spring: 3)
Satisfies Mathematics Core Requirement
Not open to students who have completed their Mathematics Core Curriculum
Requirement without permission of the Department Chairperson (except for
Psychology majors completing their second mathematics corequisite).
This course, for students in the humanities, the social sciences, School
of Education, and School of Nursing, is an introduction to finite combinatorics
and probability, emphasizing applications. Topics include finite sets and
partitions, enumeration, probability, expectation, and random variables.
Last Updated: 14-JAN-09
MT 007 Ideas in Mathematics (Spring: 3)
Satisfies Mathematics Core Requirement
Not open to students who have completed their Mathematics Core Curriculum
Requirement without permission of the Department Chairperson (except for
Psychology majors completing their second mathematics corequisite).
This course is designed to introduce the student to the spirit, beauty,
and vitality of mathematics. The emphasis is on development of ideas rather
than problem solving skills. Topics vary, but are typically chosen from
diverse areas such as geometry, number theory, computation, and graph theory.
Last Updated: 14-JAN-09
MT 100 Calculus I (Fall/Spring: 4)
Prerequisite:
Trigonometry
Corequisite:
MT 121
Satisfies Mathematics Core Requirement
MT 100 is not open to students who have completed a calculus course at the
college level. Students contemplating majors in Chemistry, Computer Science/B.S.,
Geology/Geophysics, Geophysics, Mathematics, or Physics should enroll in
MT 102.
MT 100 is a first course in the calculus of one variable intended for biology,
computer science, economics, management, and premedical students. It is
open to others who are qualified and desire a more rigorous mathematics
course at the core level. Topics include a brief review of polynomials,
trigonometric, exponential, and logarithmic functions, followed by discussion
of limits, derivatives, and applications of differential calculus to real-world
problem areas. The course concludes with an introduction to integration.
Last Updated: 11-JUN-09
MT 101 Calculus II (Fall/Spring: 4)
Prerequisite:
MT 100
Corequisite:
MT 141
Satisfies Mathematics Core Requirement
MT 101 is not open to students who have completed MT 103 or MT 105. Students
contemplating majors in Chemistry, Computer Science/B.S., Geology/Geophysics,
Geophysics, Mathematics, or Physics should enroll in either MT 103 (Spring)
or MT 105 (Fall).
MT 101 is a second course in the calculus of one variable intended for biology,
computer science, economics, management, and premedical students. It is
open to others who are qualified and desire a more rigorous mathematics
course at the core level. Topics include an overview of integration, basic
techniques for integration, a variety of applications of integration, and
an introduction to (systems of) differential equations.
Last Updated: 11-JUN-09
MT 102 Calculus I (Mathematics/Science Majors) (Fall: 4)
Prerequisite:
Trigonometry
Satisfies Mathematics Core Requirement
Not open to students who have completed a calculus course at the college
level.
MT 102 is a first course in the calculus of one variable intended for Chemistry,
Computer Science/B.S., Geology/Geophysics, Geophysics, Mathematics, and
Physics majors. It is open to others who are qualified and desire a more
rigorous calculus course than MT 100. Topics covered include the algebraic
and analytic properties of the real number system, functions, limits, derivatives,
and an introduction to integration.
Last Updated: 14-JAN-09
MT 103 Calculus II (Mathematics/Science Majors) (Spring: 4)
Prerequisite:
MT 102
Satisfies Mathematics Core Requirement
Not open to students who has completed MT 105.
MT 103 is a continuation of MT 102. Topics covered in the course include
several algebraic techniques of integration, many applications of integration,
and infinite sequences and series.
Last Updated: 11-JUN-09
MT 105 Calculus II-AP (Mathematics/Science Majors) (Fall: 3)
Not open to students who have completed MT 103.
MT 105 is a second course in the calculus of one variable intended for Chemistry,
Computer Science/B.S., Geology/Geophysics, Geophysics, Mathematics, and
Physics majors. It is designed for students who have completed either MT
101 or a year of Calculus in high school at either the AB or BC curriculum
level, but who are not yet prepared to advance to MT 202 Multivariable Calculus.
The course first reviews the primary techniques and interesting applications
of integration. The remainder of the course provides an introduction
to the topics of infinite sequences and series. Other topics may be introduced
as time permits.
Last Updated: 14-JAN-09
MT 121 Discussion/MT 100 (Fall/Spring: 0)
Corequisite:
MT 100
Recitation section, corequisite to MT 100. Discussion of problem-solving
techniques, examples, and homework in a small-class setting. One hour per
week. Sign up for a discussion section whose instructor matches your MT
100 choice.
Last Updated: 30-JAN-09
MT 141 Discussion/MT 101 (Fall/Spring: 0)
Corequisite:
MT 101
Recitation section, corequisite to MT 101. Discussion of problem-solving
techniques, examples, and homework in a small-class setting. One hour per
week. Sign up for a discussion section whose instructor matches your MT101
selection.
Last Updated: 30-JAN-09
MT 180 Principles of Statistics for the Health Sciences (Spring: 3)
Prerequisite:
Connell School of Nursing students only
Satisfies Mathematics Core Requirement
This course introduces statistics as a liberal arts discipline and applies
the principles of statistics to problems of interest to health sciences
professionals. Students will gain an understanding of statistical ideas
and methods, acquire the ability to deal critically with numerical arguments,
and gain an understanding of the impact of statistical ideas on the health
sciences, public policy and other areas of application.
Last Updated: 14-JAN-09
MT 190 Fundamentals of Mathematics I (Fall/Spring: 3)
Satisfies Mathematics Core Requirement
Restricted to Lynch School of Education students
MT 190-191 is a course sequence designed for those who plan to teach mathematics
in grades K-8. The emphasis is on building conceptual understanding of the
mathematics present in the emerging K-8 curriculum and on deepening content
knowledge. Number and number systems through the real number system will
be studied; functions and the structure of algebra will be developed. Problem
solving and reasoning, applications, and making connections will be featured.
Last Updated: 14-JAN-09
MT 191 Fundamentals of Mathematics II (Spring: 3)
Prerequisite:
MT 190
Satisfies Mathematics Core Requirement
Restricted to Lynch School of Education students
As in MT 190, the course emphasizes building conceptual understanding of
the mathematics present in the emerging K-8 curriculum and on deepening
the content knowledge. Topics drawn from geometry and measurement, data
analysis, statistics, and probability will be developed. Problem solving
and reasoning, applications, and making connections will be featured.
Last Updated: 14-JAN-09
MT 202 Multivariable Calculus (Fall/Spring: 4)
Prerequisite:
MT 101 or MT 103 or MT105 or permission of instructor
Satisfies Mathematics Core Requirement
This course is for students majoring in Chemistry, Computer Science/B.S.,
Geology-Geophysics, Geophysics, Mathematics, and Physics, as well as other
students who have completed integral Calculus.
Topics in this course include vectors in two and three dimensions, analytic
geometry of three dimensions, parametric curves, partial derivatives, the
gradient, optimization in several variables, multiple integration with change
of variables across different coordinate systems, line integrals, and Green's
Theorem.
Last Updated: 14-JAN-09
MT 210 Linear Algebra (Fall/Spring: 3)
This course is an introduction to the techniques of linear algebra in Euclidean
space. Topics covered include matrices, determinants, systems of linear
equations, vectors in n-dimensional space, complex numbers, and eigenvalues.
The course is required of mathematics majors, but is also suitable for students
in the social sciences, natural sciences, and management.
Last Updated: 14-JAN-09
MT 216 Introduction to Abstract Mathematics (Fall/Spring: 3)
This course is designed to develop the student's ability to do abstract
mathematics through the presentation and development of the basic notions
of logic and proof. Topics include elementary set theory, mappings, integers,
rings, complex numbers, and polynomials.
Last Updated: 14-JAN-09
MT 226 Probability for Bioinformatics (Spring: 3)
Prerequisite:
Calculus through Integration (e.g., MT101, MT103, or MT105)
Offered Biennially
Daniel Chambers
Last Updated: 29-OCT-09
MT 235 Mathematics for Management Science (Fall/Spring: 3)
Prerequisite:
MT 100 or equivalent, CS 021 (formerly MC 021), and EC 151 (EC 151 may be taken concurrently).
Topics include linear and integer programming, decision analysis, non-linear
optimization, and computer solutions using Excel.
Last Updated: 21-JAN-09
MT 290 Number Theory for Teachers (Spring: 3)
Prerequisite:
MT 190-191
Offered Biennially
This course is intended to focus on the wealth of topics that relate specifically
to the natural numbers. These will be treated as motivational problems to
be used in an activity-oriented approach to mathematics in grades K-9. The
course will demonstrate effective ways to use the calculator and computer
in mathematics education. Topics include prime number facts and conjectures,
magic squares, Pascal's triangle, Fibonacci numbers, modular arithmetic,
and mathematical art.
Last Updated: 26-JAN-09
MT 291 Geometry for Teachers (Spring: 3)
Prerequisite:
MT 190-191
Offered Biennially
This course is intended to fill a basic need of all teachers of grades K-9.
Geometry now occupies a significant role in the elementary mathematics curriculum.
The course will treat content, but ideas for presenting geometry as an activity-based
program will also be stressed. Topics to be covered include the geoboard
and other key manipulatives, elements of motion and Euclidean geometry,
and suggestions for using Logo as a tool to enhance teaching geometry.
Last Updated: 14-JAN-09
MT 305 Advanced Calculus (Science Majors) (Spring: 4)
Prerequisite:
MT 202. Cannot be used for major credit
MT 305 is required for Geology-Geophysics, Geophysics, and Physics majors.
It is also recommended for Chemistry majors. Topics include linear second
order differential equations series solutions of differential equations
including Bessel functions and Legendre polynomials, and solutions of the
diffusion and wave equations in several dimensions.
Last Updated: 14-JAN-09
MT 310 Introduction to Abstract Algebra (Fall/Spring: 3)
Prerequisite:
MT 210 and MT 216
This course studies four fundamental algebraic structures: groups, including
subgroups, cyclic groups, permutation groups, symmetry groups and Lagrange's
Theorem; rings, including subrings, integral domains, and unique factorization
domains; polynomials, including a discussion of unique factorization and
methods for finding roots; and fields, introducing the basic ideas of field
extensions and ruler and compass constructions.
Last Updated: 14-JAN-09
MT 320 Introduction to Analysis (Fall/Spring: 3)
Prerequisite:
MT 202 and MT 216
The purpose of this course is to give students the theoretical foundations
for the topics taught in MT 102-103. It will cover algebraic and order properties
of the real numbers, the least upper bound axiom, limits, continuity, differentiation,
the Riemann integral, sequences, and series. Definitions and proofs will
be stressed throughout the course.
Last Updated: 14-JAN-09
MT 370 Applications of Abstract Algebra (Fall: 1)
Prerequisite:
MT 310
Offered Periodically
This course is open to all majors who have had MT 310. The immediate goal
is to present some topics that extend and apply the subject matter of 310.
At the same time students may gain a deeper understanding of groups and
rings that they only imperfectly understood the first time around. A secondary
goal is for students to appreciate that the abstract concepts learned in
310 can have relevance to the outside world; for example, cryptography as
applied to modern communications, or concepts from algebra and number theory
that may be taught in the high school classroom.
Last Updated: 06-MAR-09
MT 371 Proof and Truth in Mathematics (Fall: 1)
Prerequisite:
MT 216
Offered Periodically
Can mathematical truths be deduced from a set of first principles or axioms?
The wide use of axioms in mathematics shows that many can, but what can
be proven falls short of all mathematical truths and even of all truths
in the theory of numbers. This course will explore what is known about the
limitations of the axiomatic method and computation as they relate to the
discovery of mathematical truth, and will include Godel's incompleteness
theorems.
Last Updated: 06-MAR-09
MT 372 Intro to Mathematical Problem Solving/Mathematica (Fall: 1)
Prerequisite:
MT 210 or MT 305. May be taken concurrently.
Offered Periodically
The purpose of this course is to give a directed introduction to Mathematica
(Wolfram Research Inc.), to allow students to apply this powerful tool in
such courses as mathematical modeling, ordinary and partial differential
equations, dynamical systems, probability theory, and mathematical statistics.
Topics include computer algebra, 2D/3D graphics, and the calculus and simulation
capabilities of Mathematica.
Last Updated: 06-MAR-09
MT 373 Numbers, Notations, and Recreations (Spring: 01)
Prerequisite:
MT216
Offered Periodically
This 1-credit course applies the introductory abstract mathematics of MT216
to parts of the secondary mathematics curriculum, in particular topics related
to numbers systems and notations, and recreational math problems in these
areas. Many examples which are directly useful in secondary mathematics
will be included, and we will use ideas from MT216 to explain and generalize
them. Specific topics include applications of modular arithmetic; decimal
notation (and other bases) for integers, rationals, and reals; complex numbers;
Fibonacci numbers and similar sequences; binomial coefficients and their
applications.
Last Updated: 06-OCT-09
MT 374 Pedagogical Lab for Intro to Analysis (Mt320) (Spring: 01)
Prerequisite:
MT320 (or concurrent)
Offered Periodically
This 1-credit course is designed for our current or previous MT320 (Introduction
to Analysis) students that are interested in teaching high school mathematics.
The pedagogical lab will emphasize how to apply those abstract theories
from MT320 to the teaching of high school pre-calculus and calculus. We
will also discuss various issues involved in the teaching of these courses,
such as reformed curriculums, common misconceptions, and mistakes in the
learning of this material.
Last Updated: 06-OCT-09
MT 410 Differential Equations (Fall: 3)
Prerequisite:
MT 202 and MT 210
This course is a junior-senior elective intended primarily for the general
student who is interested in seeing applications of mathematics. Among the
topics covered will be the following: first order linear equations, higher
order linear equations with constant coefficients, linear systems, qualitative
analysis of non-linear systems, and an introduction to stability and bifurcations.
Last Updated: 14-JAN-09
MT 412 Partial Differential Equations (Spring: 3)
Prerequisite:
MT 410
This course investigates the classical partial differential equations of
applied mathematics (diffusion, Laplace/ Poisson, and wave) and their methods
of solution (separation of variables, Fourier series, transforms, Green's
functions, and eigenvalue applications). Additional topics will be included
as time permits.
Last Updated: 14-JAN-09
MT 414 Numerical Analysis (Spring: 3)
Prerequisite:
MT 202, MT 210, and familiarity with using a computer
Topics include the solution of linear and nonlinear algebraic equations,
interpolation, numerical differentiation and integration, numerical solution
of ordinary differential equations, approximation theory.
Last Updated: 14-JAN-09
MT 426 Probability (Fall/Spring: 3)
Prerequisite:
MT 202, familiarity with using a computer
This course provides a general introduction to modern probability theory.
Topics include probability spaces, discrete and continuous random variables,
joint and conditional distributions, mathematical expectation, the central
limit theorem, and the weak law of large numbers. Applications to real data
will be stressed, and we will use the computer to explore many concepts.
Last Updated: 14-JAN-09
MT 427 Mathematical Statistics (Fall/Spring: 3)
Prerequisite:
MT 426 and familiarity with using a computer
Topics studied include the following: sampling distributions, parametric
point and interval estimation, hypothesis testing, goodness-of-fit, parametric
and nonparametric two-sample analysis. Applications to real data will be
stressed, and the computer will be used to explore concepts and analyze
data.
Last Updated: 14-JAN-09
MT 430 Introduction to Number Theory (Fall: 3)
Prerequisite:
MT 216
Topics covered include divisibility, unique factorization, congruences,
number-theoretic functions, primitive roots, diophantine equations, continued
fractions, quadratic residues, and the distribution of primes. An attempt
will be made to provide historical background for various problems and to
provide examples useful in the secondary school curriculum.
Last Updated: 14-JAN-09
MT 435 Mathematical Programming I (Fall: 3)
Prerequisite:
MT 210
The MT 435-436 sequence demonstrates how mathematical theory can be developed
and applied to solve problems from management, economics, and the social
sciences. Topics studied from linear programming include a general discussion
of linear optimization models, the theory and development of the simplex
algorithm, degeneracy, duality, sensitivity analysis, and the dual simplex
algorithm. Integer programming problems, and the transportation and assignment
problems are considered, and algorithms are developed for their resolution.
Other topics are drawn from game theory, dynamic programming, Markov decision
processes (with finite and infinite horizons), network analysis, and non-linear
programming.
Last Updated: 14-JAN-09
MT 440 Dynamical Systems (Spring: 3)
Prerequisite:
MT 202 and MT 410 or permission of the instructor
This course is an introduction to nonlinear dynamics and their applications,
emphasizing qualitative methods for differential equations. Topics include
fixed and periodic points, stability, linearization, parameterized families
and bifurcations, and existence and nonexistence theorems for closed orbits
in the plane. The final part of the course is an introduction to chaotic
systems and fractals, including the Lorenz system and the quadratic map.
Last Updated: 14-JAN-09
MT 451 Euclidean and Non-Euclidean Geometry (Fall/Spring: 3)
Prerequisite:
MT 216
This course surveys the history and foundations of geometry from ancient
to modern times. Topics will be selected from among the following: Mesopotamian
and Egyptian mathematics, Greek geometry, the axiomatic method, history
of the parallel postulate, the Lobachevskian plane, Hilbert's axioms for
Euclidean geometry, elliptic and projective geometry, the trigonometric
formulas, models, geometry and the study of physical space.
Last Updated: 14-JAN-09
MT 453 Euclid's Elements (Spring: 3)
Offered Periodically
This course is a close reading of Euclid's Elements in seminar style,
with careful attention to axiomatic reasoning and mathematical constructions
that build on one another in a sequence of logical arguments. We will also
emphasize clear and creative communication on mathematical ideas, with some
attention to the cultural background of the Elements and its place
in a modern education.
Mark Reeder
Last Updated: 11-JUN-09
MT 455 Mathematical Problem Solving (Spring: 3)
Prerequisite:
MT 202, MT 210, MT 216 (or equivalent mathematical background)
Corequisite:
Permission of the instructor required for students outside the LSOE.
Offered Periodically
This course is designed to deepen students' mathematical knowledge through
solving, explaining, and extending challenging and interesting problems.
Students will work both individually and in groups on problems chosen from
polynomials, trigonometry, analytic geometry, pre-calculus, one-variable
calculus, probability, and numerical algorithms. The course will emphasize
explanations and generalizations rather than formal proofs and abstract
properties. Some pedagogical issues, such as composing good problems and
expected points of confusion in explaining various topics, will come up,
but the primary goal is mathematical insight. The course will be of particular
use to future secondary math teachers.
Last Updated: 26-JAN-09
MT 460 Complex Variables (Spring: 3)
Prerequisite:
MT 202 and MT 210
This course gives an introduction to the theory of functions of a complex
variable, a fundamental and central area of mathematics. It is intended
for mathematics majors and well-prepared science majors. Topics covered
include: complex numbers and their properties, analytic functions and the
Cauchy-Riemann equations, the logarithm and other elementary functions of
a complex variable, integration of complex functions, the Cauchy integral
theorem and its consequences, power series representation of analytic functions,
the residue theorem and applications to definite integrals.
Last Updated: 14-JAN-09
MT 470 Mathematical Modeling (Spring: 3)
Prerequisite:
MT 202, MT 210, and familiarity with using a computer
This is a course primarily for mathematics majors with the purpose of introducing
the student to the creation, use, and analysis of a variety of mathematical
models and to reinforce and deepen the mathematical and logical skills required
of modelers. A secondary purpose is to develop a sense of the existing and
potential roles of both small and large scale models in our scientific civilization.
It proceeds through the study of the model-building process, examination
of exemplary models, and individual and group efforts to build or refine
models through a succession of problem sets, laboratory exercises, and field
work.
Last Updated: 14-JAN-09
MT 475 History of Mathematics (Fall: 3)
Prerequisite:
MT 310 and MT 320, one of which may be taken concurrently.
Offered Biennially
Students must be familiar with abstract algebra (groups, rings, fields)
and rigorous analysis (differentiation and integration of real valued functions,
sequences and series of functions)
This course studies the development of mathematical thought, from ancient
times to the twentieth century. Naturally, the subject is much too large
for a single semester, so we will concentrate on the major themes and on
the contributions of the greatest mathematicians. The emphasis in the course
will be on the mathematics. Students will follow the historical arguments
and work with the tools and techniques of the period being studied.
Last Updated: 06-FEB-09
MT 480 Topics in Mathematics (Spring: 3)
Prerequisite:
Varies by topics covered.
Offered Periodically
Topics for this one-semester course vary from year to year according to
the interests of faculty and students. With department permission it may
be repeated.
Last Updated: 23-JAN-09
MT 480.01 Topics in Mathematics (Spring 2009-2010: 3)
Prerequisite:
Varies by topics covered.
Prerequisites: MT 310 (or MT 816)
This course is an introduction to Cryptography with a particular emphasis
on public key cryptography. Among the topics covered are the following:
affine ciphers, the RSA algorithm, discrete logarithms, digital signatures,
primality testing, and methods of factoring large integers. The necessary
topics from number theory, especially the theory of congruences, will be
discussed as the need arises.
Last Updated: 30-JAN-09
MT 480.02 Topics in Mathematics (Spring 2009-2010: 3)
Prerequisite:
Varies by topics covered.
Prerequisites: A calculus-based course in statistical inference at the level
of MT 427, and a familiarity with using the computer to solve mathematics
problems.
Although statistical methods have become the analytical methods of choice
in areas as diverse as biomedical and environmental sciences, geophysics,
education, psychology, sociology, political science, physics, astronomy,
and communications, they are often misunderstood and misused. In this course
we will study intermediate statistics from several viewpoints, including
classical methods, graphical methods, and modern computer-intensive methods.
The multiple approach to learning should give you a deeper understanding
and appreciation for the field of statistics. Applications will be emphasized
throughout the course. Specific topics include permutation and bootstrap
methods, multiple sample analysis, least squares analysis, and contingency
table analysis.
Last Updated: 03-MAR-09
MT 499 Readings and Research (Fall/Spring: 3)
Prerequisite:
Department permission is required.
This is an independent study course, taken under the supervision of a Mathematics
Department faculty member. Interested students should see the Undergraduate
Vice Chair.
Last Updated: 30-JAN-08
MT 695 Honors Seminar (Spring: 3)
Prerequisite:
Department permission is required.
This is a seminar course required of students in the Departmental Honors
program. Other interested students may also participate in the seminar,
with permission of the instructor.
Last Updated: 14-JAN-09
MT 801 Thesis Seminar (Spring: 3)
Problems of research and thesis guidance, supplemented by individual conferences.
Last Updated: 24-NOV-09
MT 804 Analysis I (Fall: 3)
Prerequisite:
MT 320 or equivalent
The MT 804-805 sequence is intended to emphasize the basic ideas and results
of calculus and to provide an introduction to abstract analysis. The course
begins with an axiomatic introduction to the real number system. Metric
spaces are then introduced. Theoretical aspects of convergence, continuity,
differentiation, and integration are treated carefully and are studied in
the context of a metric space. The course includes an introduction to the
Lebesgue integral.
Last Updated: 14-JAN-09
MT 805 Analysis II (Spring: 3)
Prerequisite:
MT 804
This course is a continuation of MT 804.
Last Updated: 14-JAN-09
MT 814 Theory of Functions of a Complex Variable I (Fall: 3)
Prerequisite:
MT 320 or equivalent
Topics for the MT 814-815 sequence include: differentiation and integration
of a function of a complex variable, series expansion, residue theory, entire
and meromorphic functions, multiple-valued functions, Riemann surfaces,
and conformal mapping problems.
Last Updated: 14-JAN-09
MT 815 Theory of Functions of a Complex Variable II (Spring: 3)
Prerequisite:
MT 814
This course is a continuation of MT 814.
Last Updated: 14-JAN-09
MT 816 Modern Algebra I (Fall: 3)
Prerequisite:
MT 310 or permission of instructor
The MT 816-817 course sequence will study the basic structures of abstract
algebra. Topics will include groups, rings, ideal theory, unique factorization,
homomorphisms, field extensions, and Galois theory.
Last Updated: 14-JAN-09
MT 817 Modern Algebra II (Spring: 3)
Prerequisite:
MT 816
This course is a continuation of MT 816.
Last Updated: 14-JAN-09
MT 890 Graduate Teaching Seminar I (Fall/Spring: 0)
This course is designed to assist graduate students in making the transition
to the duties of a teaching assistant.
Last Updated: 10-JUN-09
MT 899 Readings and Research (Fall/Spring: 3)
Prerequisite:
Department permission is required.
This is an independent study course, taken under the supervision of a Mathematics
Department faculty member. Interested students should see the Director of
the Graduate Program.
Last Updated: 14-JAN-09
MT 903 Seminar (Spring: 3)
This seminar is required of all candidates for the M.A. degree who do not
take MT 801. It is limited to second-year graduate students.
Last Updated: 09-JUN-09