Mathematics |
MATH 301 - Elementary Math I
Credits:
4.00
Beginning algebra including integer operations, solving
linear equations, graphing linear functions, solving
linear inequalities, systems of linear equations,
polynomials, rational expressions and equations, and
exponents and radicals. May not be taken for credit toward
a bachelor's degree.
MATH 302 - Elementary Math II
Credits:
4.00
Review of elementary algebra, exponents, polynomials,
factoring, rational exponents, and absolute value. Solving
linear and quadratic equations and inequalities; systems of
equations; radical equations. Linear functions and related
notions; quadratic functions. May not be taken for credit
toward a bachelor's degree. Prereq: MATH 301 or the
equivalent.
MATH 400 - Freshman Seminar
Credits:
1.00
A seminar experience that presents a mathematical culture
associated with first-year college mathematics, including
the ideas of abstraction, theorem and proof, ad that
provides a perspective of the diversity of mathematical
areas of research and their interrelationships. Emphasis is
on reading and writing mathematics. Cr/F.
MATH 418 - Analysis and Applications of Functions
Credits:
4.00
Analysis and applications of algebraic and transcendental
functions, with special emphasis on exponential,
logarithmic, and trigonometric functions. Graphical
analysis. Written projects are required on some or all of
the following topics: rates of change, optimization,
logarithmic or exponential modeling, and trigonometric
functions. Intended for students planning to take MATH 425.
Prereq: MATH 302 or equivalent. Not offered for credit if
credit is received for MATH 424 or MATH 425.
MATH 420 - Finite Mathematics
Credits:
4.00
Topics selected from probability, systems of linear
equations, matrix algebra, linear programming, mathematics
of finance. Not a preparation for calculus. Prereq: MATH
302 or the equivalent. Not offered for credit to
mathematics majors.
MATH 421 - Pathways between Mathematics and the Arts
Credits:
4.00
Exploration of the interaction between mathematics and the
arts on numerous levels. The course builds on basic
knowledge of elementary number systems to illuminate such
topics symmetry, fractals, light, color, sound structures
and musical materials. Student immediately apply new
knowledge and techniques to make computer generated 2-D and
3-D images, animations and sound/music.
MATH 424A - Calculus for Social Sciences
Credits:
4.00
Rational, exponential and logarithmic functions; associated
derivatives and their applications; associated
antiderivatives and their applications. Applications focus
on contexts relevant to majors in the College of Liberal
Arts and the Whittemore School of Business and Economics.
Prereq: MATH 418 or equivalent.
Not offered for credit to
CEPS majors.
Not offered for credit if credit is received
for MATH 425.
Students wanting a two-semester calculus
course are strongly advised to take MATH 425-426. Those
students who successfully complete MATH 424A and
subsequently wish to continue their study of mathematics
with MATH 426 are encouraged to complete supplementary
modules available from the Mathematics Center (MaC).
MATH 424B - Calculus for Life Sciences
Credits:
4.00
Rational, exponential and logarithmic functions; associated
with derivatives and their applications; associated with
antiderivatives and their applications. Applications focus
on contexts relevant to majors in the College of Life
Sciences and Agriculture.
Prereq: Math 418 or qualification
through the placement evaluation. Students enrolling in
MATH 424B are required to take a placement evaluation.
Those unprepared for MATH 424B will be required to take
MATH 418.
Not offered for credit for CEPS majors.
Not
offered for credit if credit is received for MATH 425.
Students wanting a two-semester calculus course are
strongly advised to take MATH 425-426. Those students who
successfully complete MATH 424B and subsequently wish to
continue their study of mathematics with MATH 426 are
encouraged to complete supplementary modules available from
the Mathematics Center (MaC).
MATH 425 - Calculus I
Credits:
4.00
Calculus of one variable covering limits, derivatives of
algebraic, trigonometric, exponential, and logarithmic
functions; applications include curve sketching, max-min
problems, related rates, and volume and area problems.
Prereq: completing MATH 418 with a grade of C or better or
qualifying with the placement evaluation. (Not offered for
credit if credit is received for MATH 424.)
MATH 425H - Honors/Calculus I
Credits:
4.00
Calculus of one variable covering limits, derivatives of
algebraic, trigonometric, exponential, and logarithmic
functions; applications include curve sketching, max-min
problems, related rates, and volume and area problems.
Prereq: completing MATH 418 with a grade of C or better or
qualifying with the placement evaluation. (Not offered for
credit if credit is received for MATH 424.) Enrollment in
MATH 425H requires concurrent enrollment in PHYS 407H.
MATH 426 - Calculus II
Credits:
4.00
Second course in calculus of one argument, techniques and
applications of integration, polar coordinates, and
series. Prereq: MATH 425.
MATH 426H - Honors/Calculus II
Credits:
4.00
Second course in calculus of one argument, techniques and
applications of integration, polar coordinates, and
series. Prereq: MATH 425. Enrollment in MATH 426H requires
concurrent enrollment in PHYS 408H.
MATH 439 - Statistical Discovery for Everyone
Credits:
4.00
Introduces the framework and concepts for learning with
data. Emphasis on statistical discovery in everyday life
and on drawing valid conclusion from data. Topics include:
good and bad data, data ethics, how to conduct a valid
survey, how to describe a population distribution; when to
believe a poll; how to design an experimental study; how to
avoid ambiguous results caused by "lurking" variables; how
to make inference about an entire population based on a
sample; how to describe relationships among variables; an
understanding of the question of causation and chance in
everyday life and in scientific studies, as well as the use
and misuse of statistics in explaining what is statistical
significance. This course has an activity-based learning
component with lab exercises using statistical software for
calculations without assuming a calculus background. The
course may be used as a preparation for a more technical
introductory statistics course. Not offered for credit if
credit is received for ADM 430, ADMN 420, BIOL 528, EREC
525, HHS 540, MATH 539, MATH 644, PSYC 402, SOC 502.
Science and Engineering students should take MATH 539 or
MATH 644 according to their programs.
MATH 444 - Excursions in Quantitative Reasoning
Credits:
4.00
Problems involving quantitative reasoning (most are
nontraditional, some are fun, while others are
interdisciplinary) designed to inspire curiosity encourages
students to formulate and evaluate questions, all the while
slowly drawing them into the process of scholarly
investigation. In this regard, in addition to traditional
mathematics homework, students need to do research outside
of class to write and present projects.
MATH 445 - Mathematics and Applications with MATLAB
Credits:
4.00
Through the use of the MATLAB computation software, this
course reinforces and builds on a student's mathematics
foundation and previews more advanced mathematical
concepts. The power and limitations of modern computational
algorithms to solve real world problems are introduced and
shown to influence nearly every aspect of modern society.
The state-of-the-art computational tools afforded by MATLAB
provide the student with a strategy for enhancing their
knowledge and comprehension in susequent Science,
Engineering, or Technology themed courses. Prereq: MATH 418
or permission.
MATH 525 - Linearity I
Credits:
6.00
Examines the fundamental role that linear models play in
science and engineering; and the role of linearization in
understanding nonlinear phenomena. Models are considered
along several conceptual axes: discrete to continuous,
one-dimensional to multidimensional, and static to dynamic,
with an emphasis on the former. Mathematical areas of
coverage include matrix algebra, concepts from calculus of
several variables, difference equations, and linear
transformations. Prereq: MATH 426, permission. Lab.
MATH 526 - Linearity II
Credits:
6.00
Continuation of study of linear models and the process of
linearization begun in MATH 525, with an emphasis on
models of dynamic phenomena. Additional mathematical areas
of coverage include differential equations, eigenvalue and
eigenvector analysis, phase plane analysis, and additional
concepts from vector calculus. Prereq: MATH 525,
permission. Lab.
MATH 527 - Differential Equations with Linear Algebra
Credits:
4.00
Fundamental methods of solving first-order equations,
essentials of matrix algebra; higher-order linear
equations, and linear systems; series solutions; Laplace
transforms; selected applications. Prereq: MATH 426.
MATH 528 - Multidimensional Calculus
Credits:
4.00
Partial differentiation; composite functions and chain
rules; maximum and minimum; transformations; vector
algebra; vector functions; gradient, divergence, and curl;
curves and surfaces; multiple, line, and surface integrals;
divergence, Green's and Stoke's theorem. Prereq: MATH 426.
MATH 531 - Mathematical Proof
Credits:
4.00
Introduces reading and writing proofs in mathematics. The
basic language of mathematics common to all branches of
the subject, especially set theory and basic logic. Prereq:
MATH 425; or permission. Writing intensive.
MATH 532 - Discrete Mathematics
Credits:
4.00
Counting principles (including permutations, combinations,
pigeonhole principle, inclusion-exclusion principle);
big-O relation; graphs, trees, and related topics. Prereq:
MATH 531.
MATH 539 - Introduction to Statistical Analysis
Credits:
4.00
A first course introducing concepts of probability and
scientific methods for data analysis. Exploratory data
analysis, survey sampling, probability, discrete and
continuous distributions, confidence intervals, hypothesis
testing, comparing samples, linear regression, analysis of
variance. Statistical software is used.
Prereq: MATH 425;
or permission.
Not offered for credit if credit is
received for MATH 644.
Offered primarily for mathematics
majors; engineering majors should take MATH 644.
MATH 545 - Introduction to Linear Algebra
Credits:
4.00
Designed to reinforce ideas seen throughout the mathematics
curriculum. Centered on a study of vector spaces and
linear systems, beginning with a brief focus on systems of
linear equations and progressing to a full discussion of
linear transformation and vector spaces. The course
includes a survey of properties of matrices, such as rank,
kernel, eigenvalues, eigenvectors, and diagonalization.
Prereq: MATH 426 Writing intensive.
No credit offered if
credit is received for MATH 645 or MATH 762.
MATH 601 - Exploring Mathematics for Teachers I
Credits:
4.00
Provides prospective elementary teachers with the
opportunity to explore and master concepts involving
number systems and operations, data analysis and
probability. Additional topics may include geometry,
measurement, and algebraic thinking. Mathematical
reasoning, problem solving, and the use of appropriate
manipulatives and technology are integrated throughout the
course. Readings, class discussions, and assignments focus
on mathematics content as well as applicable theories of
learning, curriculum resources, and state and national
recommendations. The course models instructional techniques
that can be adapted to the elementary curricula.
Prereq:
EDUC 500.
(Not offered for credit if credit is received
for MATH 621 or,- 623;
not offered for credit to CEPS
majors.)
MATH #602 - Exploring Mathematics for Teachers II
Credits:
4.00
Provides prospective elementary teachers with the
opportunity to explore and master concepts involving
geometry, measurement, and algebraic thinking. Mathematical
reasoning, problem solving, and the use of appropriate
manipulatives and technology are integrated throughout the
course. Readings, class discussions, and assignments focus
on mathematics content as well as applicable theories of
learning, curriculum resources, and state and national
recommendations. The course models instructional techniques
that can be adapted to the elementary curricula.
Prereq:
EDUC 500.
(Not offered for credit if credit is received for
MATH 621 or,- 622, 721;
not offered for credit to CEPS
majors.)
MATH 619 - Historical Foundations of Mathematics
Credits:
4.00
Historical development of number theory, geometry,
probability, algebra, and analysis. Study of the
significant mathematical contributions to these topics made
by prominent mathematicians spanning several historical
periods. Prereq: MATH 531 or 545.
MATH 621 - Number Systems for Teachers
Credits:
4.00
Problem solving; counting and set concepts, number systems
(whole numbers, integers, rational, and real numbers);
number theory; estimation and mental calculation
techniques; and applications requiring calculators and
computers. Manipulatives and models are used in a lab
setting to illustrate the concepts and properties of the
number systems and teach number sense.
Prereq:
permission.
Not offered for credit to mathematics majors,
except those in elementary or middle school options of the
B.S. in Mathematic Education degree program.
Offered in
alternate years in the fall semester.
MATH 622 - Geometry for Teachers
Credits:
4.00
Properties of two- and three dimensional figures;
tessellations; symmetry; LOGO computer language;
nonstandard, English, and metric units of measure; area and
perimeter; volume and surface area; estimations and
approximations of measurements; constructions; congruence
and similarity mappings; problem solving using geometric
and algebraic skills; and applications requiring
calculators and computers. Manipulatives and models are
used in a lab setting to illustrate concepts and properties
of geometry.
Prereq: MATH 621 or permission.
Not offered
for credit to mathematics majors, except those in the
elementary or middle school options of the B.S. in
Mathematics Education degree program.
Offered in alternate
years in the spring semester following MATH 621.
MATH 623 - Topics in Mathematics for Teachers
Credits:
4.00
Logic (valid and invalid forms of reasoning); descriptive
statistics (graphs, measures of central tendency, measures
of variation); inferential statistics (samplings,
distributions, measures of relative standing, simulations);
probability (experimental, geometrical, and theoretical);
permutations and combinations; problem solving using skills
from statistics and probability; mathematical connections
using computer software; and applications requiring
calculators and computers. Prereq: MATH 621; or permission.
Not offered for credit to mathematics majors, except those
in the elementary or middle school options of the B.S. in
Mathematics Education degree program.
Offered in alternate
years in the fall semester following MATH 622.
MATH 624 - Analysis of Secondary School Mathematics
Credits:
4.00
Examines concepts from calculus and pre-calculus
mathematics with an emphasis on connecting and logically
refining the concepts of function, limit, sequences,
series, and probability. Includes a deeper analysis of
problems and topics drawn from secondary school mathematics
with the kind of mathematical knowledge and sophistication
that the student has gained from other collegiate
mathematics courses. Proofs for many of the theorems that
are typically introduced in a non-rigorous fashion in
calculus are studied. Prereq: EDUC 500, MATH 425 and 545
(or equivalent); or permission. Offered in alternate years
in the spring semester following MATH 623.
MATH 644 - Statistics for Engineers and Scientists
Credits:
4.00
Introduces the design of controlled experiments and the
collection and analysis of scientific data. Use of a
statistical software package is an integral part of the
course; interpreting and drawing conclusions from standard
software output is emphasized. Graphical data analysis,
statistical process control, regression and correlation,
multifactor experimental designs, confidence intervals,
hypothesis testing. Not offered for credit if credit is
received for MATH 539. Prereq: MATH 426.
MATH 645 - Linear Algebra for Applications
Credits:
4.00
Fundamental notions of vector space theory, linear
independence, basis, span, scalar product, orthogonal
bases. Includes a survey of matrix algebra, solution of
systems linear equations, rank, kernel, eigenvalues and
eigenvectors, the LU- and QR-factorizations, and least
squares approximation. Selected applications in
mathematics, science, engineering and business. Prereq:
MATH 426. (Not offered for credit if credit is received for
MATH 545 or MATH 762.)
MATH 646 - Introduction to Partial Differential Equations
Credits:
4.00
Introduces the solution of partial differential equations.
Models arising from initial-boundary-value problems of
mathematical physics and Sturm-Liouville problems are
examined; solution techniques include separation of
variables, Bessel functions, series expansions by
orthogonal functions, and numerical methods. Prereq: CS 410
or 415; MATH 527; 528; 645; /or permission.
MATH 647 - Complex Analysis for Applications
Credits:
4.00
Complex numbers, analytic functions, Cauchy-Riemann
equations, conformal mapping, contour integration,
Cauchy's integral formula, infinite series, residue
calculus, Fourier and Laplace transforms. Prereq: MATH 528.
(Not offered for credit if credit is received for MATH 788.)
MATH 656 - Introduction to Number Theory
Credits:
4.00
Unique factorization, arithmetic functions, linear and
quadratic congruence's, quadratic reciprocity law,
quadratic forms, introduction to algebraic numbers. Prereq:
MATH 531. Offered in alternate years.
MATH 657 - Geometry
Credits:
4.00
Advanced approach to fundamental properties of Euclidean
and other geometries. Prereq: MATH 531. Writing intensive.
MATH 658 - Topics in Geometry
Credits:
4.00
Topics selected from among projective geometry, finite
geometrics, convexity, transformational geometry,
non-Euclidean geometry, and other areas of elementary
geometry within the framework of modern mathematics.
Prereq: MATH 657. Offered in alternate years.
MATH 696 - Independent Study
Credits:
1.00 to 4.00
Individual projects of study developed by the student and
a faculty sponsor. Intended for students with superior
scholastic achievement. May be repeated up to 8 credits.
May be taken as writing intensive. Prereq: a written
proposal, including goals and assessment, endorsed by a
faculty sponsor and approved by the department chairperson.
MATH 696W - Independent Study
Credits:
1.00 to 4.00
Individual projects of study developed by the student and
a faculty sponsor. Intended for students with superior
scholastic achievement. May be repeated up to 8 credits.
May be taken as writing intensive. Prereq: a written
proposal, including goals and assessment, endorsed by a
faculty sponsor and approved by the department chairperson.
Writing intensive.
MATH 699 - Internship Experience
Credits:
1.00
Provides the opportunity to apply and enhance knowledge in
a setting associated with future professional employment.
A written mid-semester report is required as well as a
final report along with an oral presentation that is open
to other undergraduates. Prereq: A written proposal,
endorsed by a faculty sponsor and approved by the
department chairperson (or designee), that outlines the
goals, academic merit and assessment of the work
experience. May be repeated up to 4cr. Only open to Math
majors. Cr/F.
MATH 700 - Introduction to Mathematics Education
Credits:
4.00
General background information about mathematics
education, such as theories of learning and teaching
mathematics, mathematics curricula, classroom management,
and techniques for the teaching and learning of mathematics
that are common to all levels of mathematics education
K-12. Prereq: MATH 426 and EDUC 500; or permission.
MATH 703 - Teaching of Mathematics, K-6
Credits:
4.00
Methods of teaching mathematics at the elementary school
level; uses of technology, manipulatives, models, and
diagrams; developing unit and lesson plans; assessment ;
instructional formats; teaching reading and writing in
mathematics.
Prereq: MATH 621 (or MATH 601) and MATH 700;
or permission.
MATH 708 - Teaching Middle School Mathematics
Credits:
4.00
Methods of teaching mathematics at the middle school level;
uses of technology, manipulatives, models, and diagrams;
developing unit and lesson plans; assessment; instructional
formats; teaching reading and writing in mathematics.
Prereq: MATH 700; or permission. Offered in alternate years
in the spring semester.
MATH 709 - Teaching of Mathematics, 7-12
Credits:
4.00
Methods of teaching content at the secondary school level;
uses of technology, manipulatives, models, and diagrams;
developing unit and lesson plans; assessment; instructional
formats; teaching reading and writing in mathematics.
Prereq: MATH 700; or permission.
Offered in alternate
years in the spring semester.
MATH 736 - Advanced Statistical Methods for Research
Credits:
4.00
An introduction to multivariate statistical methods,
including principal components, discriminant analysis,
cluster analysis, factor analysis, multidimensional
scaling, and MANOVA. Additional topics include generalized
linear models, general additive models, depending on the
interests of class participants. The use of statistical
software, such as JMP, S PLUS, or R, is fully integrated
into the course. Prereq: MATH 739.
MATH 737 - Statistical Methods for Quality Improvement
Credits:
4.00
Introduces scientific data collection and analysis with an
emphasis on industrial and service provider applications.
Topics include: descriptive and graphical statistical
methods; confidence intervals and hypothesis testing;
regression; ANOVA; statistical process control (SPC);
failure modes and effects analysis (FMEA); Six-Sigma
concepts and methods; introduction to Reliability; quality
tools, MSA, and process capability studies; introduction to
Lean methodology, such as 5S, Kaizen, and VSM. Use of a
software package is an integral part of the course. Prereq:
MATH 644.
MATH 739 - Applied Regression Analysis
Credits:
4.00
Statistical methods for the analysis of relationships
between response and input variables: simple linear
regression, multiple regression analysis, residual analysis
and model selection, multi-collinearity, nonlinear curve
fitting, categorical predictors, analysis of variance,
analysis of covariance, examination of validity of
underlying assumptions, logistic regression analysis.
Emphasizes real applications with use of statistical
software. Prereq: MATH 539 (or 644). Writing intensive.
MATH 740 - Design of Experiments I
Credits:
4.00
Course in design of experiments with applications to
quality improvement in industrial manufacturing,
engineering research and development, or research in
physical and biological sciences. Experimental factor
identification, statistical analysis and modeling of
experimental results, randomization and blocking, full
factorial designs, random and mixed effects models,
replication and sub-sampling strategies, fractional
factorial designs, response surface methods, mixture
designs, and screening designs. Focuses on various
treatment structures for designed experimentation and the
associated statistical analyses. Use of statistical
software. Prereq: MATH 539 (or 644); or permission.
MATH 741 - Survival Analysis
Credits:
4.00
Explorations of models and data-analytic methods used in
medical, biological, and
reliability studies. Event-time
data, censored data, reliability models and methods,
Kaplan-Meier estimator, proportional hazards, Poisson
models, loglinear models.The use of statistical software,
such as SAS, JMP, or R, is fully integrated into the
course.
Prereq: MATH 739.
(Offered in alternate years in
the spring semester.)
MATH 743 - Time Series Analysis
Credits:
4.00
An introduction to univariate time series models and
associated methods of data analysis and inference in the
time domain and frequency domain. Topics include: auto
regressive (AR), moving average (MA), ARMA and ARIMA
processes, stationary and non-stationary processes,
seasonal ARIMA processes, auto-correlation and partial
auto-correlation functions, identification of models,
estimation of parameters, diagnostic checking of fitted
models, forecasting, spectral density function, periodogram
and discrete Fournier transform, linear filters, parametric
spectral estimation, dynamic Fournier analysis. Additional
topics may include wavelets and long memory processes
(FARIMA) and GARCH Models. The use of statistical software,
such as JMP, or R, is fully integrated into the course.
Prereq: MATH 739. Offered in alternate years in the spring
semester.
MATH 744 - Design of Experiments II
Credits:
4.00
A second course in design of experiments, with applications
in quality improvement and industrial manufacturing,
engineering research and development, research in physical
and biological sciences. Covers experimental design
strategies and issues that are often encountered in
practice: complete and incomplete blocking, partially
balanced incomplete blocking (PBIB), partial confounding,
intra and inter block information, split plotting and strip
plotting, repeated measures, crossover designs, Latin
squares and rectangles, Youden squares, crossed and nested
treatment structures, variance components, mixed effects
models, analysis of covariance, optimizations, space
filling designs, and modern screening design strategies.
Prereq: MATH 740; or permission.
MATH 745 - Foundations of Applied Mathematics I
Credits:
4.00
An introduction to Partial Differential Equations (PDEs)
and associated mathematical methods and the analytical
foundation for applied mathematics. Topics include: PDE
classification, superposition, separation of variables,
orthonormal functions, completeness, convergence, Fourier
Series, Sturm-Liouville eigenvalue problems, and
eigenfunctions. Methods are introduced for the analysis and
solution of boundary value problems, in particular, the
Heat, Wave, and Laplace equations. Prereq: MATH 527 and
528; or equivalent.
MATH 746 - Foundations of Applied Mathematics II
Credits:
4.00
An introduction to special functions, asymptotic analysis,
and transform methods applied to partial differential
equations. Topics include: Boundary value problems in
cylindrical coordinates, the Bessel equation and Bessel
functions, Fourier-Bessel expansions in cylindrically
symmetric spatial domains, the Fourier Transform, the
Hilbert Transform, Cosine and Sine Transforms, problems on
semi-infinite intervals, and Asymptotic Analysis. Prereq:
MATH 527 and MATH 528; or equivalent.
MATH 747 - Introduction to Nonlinear Dynamics and Chaos
Credits:
4.00
The mathematics of chaos and nonlinear dynamics. Topics
include linear and nonlinear systems of ordinary
differential equations, discrete maps, chaos, phase plane
analysis, bifurcations and computer simulations. Prereq:
MATH 527, 528, and 645.
MATH 753 - Introduction to Numerical Methods I
Credits:
4.00
Introduces mathematical algorithms and methods of
approximation. Topics include a wide survey of
approximation methods. Methods examined include polynomial
interpolation, root finding, numerical linear algebra,
numerical integration, and the approximation of
differential equations. Included in each case is a study of
the accuracy and stability of a given technique, as well as
its efficiency. Prereq: MATH 426; CS 410.
MATH 755 - Probability with Applications
Credits:
4.00
Introduces the theory, methods, and applications of
randomness and random processes. Probability concepts,
random variable, expectation, discrete and continuous
probability distributions, joint distributions, conditional
distributions; moment-generating functions, convergence of
random variables. Prereq: MATH 528 and 539 (or 644).
MATH 756 - Principles of Statistical Inference
Credits:
4.00
Introduces the basic principles and methods of statistical
estimation and model fitting. One- and two-sample
procedures, consistency and efficiency, likelihood methods,
confidence regions, significance testing, Bayesian
inference, nonparametric and re-sampling methods, decision
theory. Prereq: MATH 755; or permission.
MATH 761 - Abstract Algebra
Credits:
4.00
Basic properties of groups, rings, fields, and their
homomorphism's. Prereq: MATH 531. Writing intensive.
MATH 762 - Linear Algebra
Credits:
4.00
Vector spaces over arbitrary fields, linear
transformations and their relationship with matrices,
eigenvalues and eigenvectors, the rational and Jordan
canonical forms for linear transformations. Prereq: MATH 761
MATH 767 - One-Dimensional Real Analysis
Credits:
4.00
Theory of limits, continuity, differentiability, and
integrability. Prereq: MATH 531. Writing intensive.
MATH 776 - Logic
Credits:
4.00
Examination of the basic notions of soundness and
completeness, first for sentential and then for
propositional logic. Turning to the question of decision
procedures for logical formulae, the concept of recursive
function, which emerges in the work of Church and Turning,
provides the essential link between logic and theory of
computation. The course culminates with Godel's
Incompleteness Theorems, which demonstrate the intrinsic
limitations of the logical method. Prereq: MATH 531.
Offered in alternate years.
MATH 783 - Set Theory
Credits:
4.00
Axiomatic set theory, including its history. Cantor's
theory of infinite cardinal and ordinal numbers seemed
laden with contradictions and paradoxes. A satisfactory
treatment of these difficulties came with the axiomatic set
theory of Zermelo and Fraenkel. This course develops the
Zermelo-Fraenkel axioms and examines cardinal and ordinal
arithmetic in the context they provide. The course then
investigates the consequences of various additional axioms
extending Zermelo-Fraenkel, such as the Axiom of Choice,
the Continuum Hypothesis, large cardinal axioms of
determinacy. Prereq: MATH 531. Offered in alternate years.
MATH 784 - Topology
Credits:
4.00
Open sets, closure, base, and continuous functions;
connectedness, compactness, separation axioms, and
metrizability. Prereq: MATH 531. Writing intensive.
MATH 788 - Complex Analysis
Credits:
4.00
Complex functions, sequences, limits, differentiation and
Cauchy-Riemann equations, elementary functions, Cauchy's
theorem and formula, Taylor's and Laurent's series,
residues, conformal mapping. Prereq: MATH 767. Not offered
for credit if credit is received for MATH 647.
MATH 796 - Topics
Credits:
1.00 to 4.00
New or specialized courses not covered in regular course
offerings. Prereq: permission of instructor. May be
repeated.
MATH 797 - Senior Seminar
Credits:
4.00
Exploration of mathematical topics beyond the student's
previous coursework in the seminar format. The course
focus is on independent research, collaborative work and
classroom engagement; oral presentations and written work
are required. Prereq: senior standing.
MATH 798 - Senior Project
Credits:
4.00
Students work either individually or as a group under the
direction of a faculty sponsor to plan and carry out an
independent research project resulting in a written report
and presentation to the department. Prereq: Senior standing
in the department; a written proposal approved by a faculty
sponsor and by the department chairperson (or designee).
MATH 799 - Senior Thesis
Credits:
2.00 or 4.00
Students work under the direction of a faculty sponsor to
plan and carry out independent research resulting in a
written thesis. Required for honors-in-major. Prereq:
senior standing; a written proposal endorsed by a faculty
sponsor and approved by the department chairperson (or
designee). May be repeated up to 4 credits. Writing
intensive.