Courses - Spring 2025
MATH003
Developmental Mathematics
Credits:
3
Grad Meth:
S-F
A review of Intermediate High School Algebra intended for students preparing for one of the credit bearing Fundamental Studies Math Courses. It is taught in special computer labs using a self-paced computer program. The curriculum will be geared toward the student's level of algebra skills and eventual goals. There is a special fee for the course that may be applied in addition to the regular tuition charge. Students should refer to the schedule of classes for details on fees as they apply to a particular semester. The course does not carry any credit toward any degree at the University. The course is repeatable. Topics will be chosen from exponents, polynomials, linear equations, quadratic equations as well as polynomial, rational, exponential and logarithm functions and elementary probability or statistics, depending on the student.
Students must pay a special math fee.
MATH007
Algebra for MATH 107
Credits:
3
Grad Meth:
Reg, P-F, Aud
A review of Intermediate High School Algebra intended for students preparing for MATH107. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH107, the same semester, which also meets 5 days per week. Continuation in MATH107 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include linear equations, linear inequalities, operations on polynomials, factoring, solutions of quadratic equations, as well as exponential and logarithm functions. MATH007 does not carry any credit toward any degree at the University, nor is it graded. It leads to either MATH107 or MATH003, both of which are graded.
MATH013
Algebra for MATH 113
Credits:
3
Grad Meth:
Reg, P-F, Aud
A review of Intermediate High School Algebra intended for students preparing for MATH113. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH113, the same semester, which also meets 5 days per week. Continuation in MATH113 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include exponents, polynomials, linear equations, quadratic equations, as well as polynomial, rational, exponential, and logarithm functions, and trigonometry. MATH013 does not carry any credit toward any degree at the University, nor is it graded. It leads directly to MATH113 (or MATH107), or MATH003, all of which are graded.
MATH015
Algebra for MATH 115
Credits:
3
Grad Meth:
Reg, P-F, Aud
A review of Intermediate High School Algebra intended for students preparing for MATH115. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH115, the same semester, which also meets 5 days per week. Continuation in MATH115 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include exponents, polynomials, linear equations in one and two variables, quadratic equations, as well as polynomial, rational, exponential, logarithm functions and trigonometry. MATH015 does not carry any credit toward any degree at the University, nor is it graded. It leads directly to MATH115 (or MATH107 or MATH113), or MATH003, all of which are graded.
MATH107
Introduction to Math Modeling and Probability
Prerequisite: Must have math eligibility of MATH107 or higher; and math eligibility is based on Math Placement Exam or successful completion of MATH003 with appropriate eligibility.
Restriction: Not open to students majoring in mathematics, engineering, business, life sciences, and the physical sciences; must not have completed STAT100, MATH113, MATH120, MATH135, MATH136 or MATH140 with a C- or better; must not have completed any MATH or STAT course with a prerequisite of MATH120, MATH136, or MATH140.
Formerly: MATH110 and MATH111.
A goal is to convey the power of mathematics as shown by a variety of problems which can be modeled and solved by quantitative means. Also included is an introduction to probability. Topics include data analysis, equations, systems of equations, inequalities, elementary linear programming, Venn diagrams, counting, basic probability, permutations, combinations, tree diagrams, standard normal and normal distributions. The mathematics of finance is covered. The course includes problem solving and decision making in economics, management, and social sciences.
MATH113
College Algebra and Trigonometry
Prerequisite: Must have math eligibility of MATH113 or higher; and math eligibility is based on the Math Placement Exam or the successful completion of MATH 003 with appropriate eligibility.
Restriction: Must not have completed MATH115, MATH120, MATH135, MATH136 or MATH140 with a grade of C- or higher; and must not have completed any course with a prerequisite of MATH120, MATH130, MATH136, or MATH140.
Credit only granted for: MATH113 or MATH115.
Topics include elementary functions including graphs and applications of: polynomial, rational, exponential, and logarithmic functions. Systems of equations and applications. Trigonometric functions: angle and radian measure, graphs and applications.
MATH115
Precalculus
Prerequisite: Must have math eligibility of MATH115 or higher; and math eligibility is based on the Math Placement Exam or the successful completion of MATH003 with appropriate eligibility. Or MATH113.
Restriction: Must not have completed MATH140 with a grade of C- or better; and must not have completed any MATH or STAT course with a prerequisite of MATH140 or MATH141.
Credit only granted for: MATH113 or MATH115.
Preparation for MATH120, MATH130 or MATH140. Elementary functions and graphs: polynomials, rational functions, exponential and logarithmic functions, trigonometric functions. Algebraic techniques preparatory for calculus.
Preparation for MATH220 or MATH140. If purchasing used books additional software may be required.
MATH120
Prerequisite: 1 course with a minimum grade of C- from (MATH113, MATH115). Or must have math eligibility of MATH120 or higher; and math eligibility is based on the Math Placement Test.
Restriction: Not open to students majoring in mathematics, engineering, the biological sciences, biochemistry, chemistry, or the physical sciences; Must not have completed MATH130, MATH136 or MATH140 with a grade of C- or higher.
Formerly: MATH220.
Basic ideas of differential and integral calculus, with emphasis on elementary techniques of differentiation and applications.
MATH121
Elementary Calculus II
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH120, MATH130, MATH136, or MATH140.
Restriction: Not open to students majoring in mathematics, engineering, the biological sciences, biochemistry, chemistry, or the physical sciences; Must not have completed MATH141 with a grade of C- or higher.
Formerly: MATH221.
Trigonometric functions, techniques of integration, infinite series, differential equations, probability.
MATH135
Prerequisite: Minimum grade of C- in MATH113 or MATH115; or must have math eligibility of MATH120 or higher; and math eligibility is based on the Math Placement Test.
Restriction: Must be in the Biological Sciences or Neuroscience major; and not open to students majoring in mathematics, engineering, or the physical sciences.
Basic discrete mathematics, with emphasis on relevant models and techniques to the life sciences.
MATH136
Calculus for Life Sciences
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH135.
Restriction: Must be in the Biological Sciences or Neuroscience major; Must not have completed MATH140 with a grade of C- or higher.
Continuation of MATH135, including basic ideas of differential and integral calculus, with emphasis on elementary techniques and applications to the life sciences.
MATH140
Prerequisite: Minimum grade of C- in MATH115.
Introduction to calculus, including functions, limits, continuity, derivatives and applications of the derivative, sketching of graphs of functions, definite and indefinite integrals, and calculation of area. The course is especially recommended for science, engineering and mathematics majors.
Graphing calculators, or computers, etc., with software appropriate for graphing non-trivial functions and doing non-trivial calculations, will be needed.
MATH141
Calculus II
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH140.
Continuation of MATH140, including techniques of integration, improper integrals, applications of integration (such as volumes, work, arc length, moments), inverse functions, exponential and logarithmic functions, sequences and series.
Graphing calculators, or computers, etc., with software appropriate for graphing non-trivial functions and doing non-trivial calculations, will be needed.
MATH141H
Calculus II
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH140.
Continuation of MATH140, including techniques of integration, improper integrals, applications of integration (such as volumes, work, arc length, moments), inverse functions, exponential and logarithmic functions, sequences and series.
Restrictions: For Honors College students only. Graphing calculators, or computers, etc., with software appropriate for graphing non-trivial functions and doing non-trivial calculations, will be needed.
MATH206
Introduction to Matlab
Credits:
1
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH136, MATH140).
This course is intended to prepare students for subsequent courses requiring computation with MATLAB. Covers basics of MATLAB including simple commands, variables, solving equations, graphing differentiation and integration, matrices and vectors, functions, M-files and fundamentals of programming in the MATLAB environment. When offered in Winter and Summer terms, the course is offered in a format suitable for online distance learning.
MATH212
Elements of Numbers and Operations
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Must have completed one year of college preparatory algebra.
Restriction: Must be in one of the following programs (Early Childhood Education; Special Education; Elementary Education).
Reviews and extends topics of arithmetic and number theory related to the elementary school curriculum, particularly number systems and operations with natural numbers, integers, and rationals.
MATH213
Elements of Geometry and Measurement
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH212.
Restriction: Must be in one of the following programs (Early Childhood Education; Special Education; Elementary Education).
Properties of geometric objects in two and three dimensions; parallel lines, curves and polygons; ratio, proportion, similarity; transformational geometry and measurement, constructions, justifications and proofs.
MATH214
Elements of Probability and Statistics
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH212.
Restriction: Must be in one of the following programs (Early Childhood Education; Special Education; Elementary Education).
Permutations and combinations; probability; collecting and representing data; using statistics to analyze and interpret data.
MATH240
Introduction to Linear Algebra
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH131, MATH141).
Credit only granted for: MATH240, MATH341, or MATH461.
Basic concepts of linear algebra: vector spaces, applications to line and plane geometry, linear equations and matrices, similar matrices, linear transformations, eigenvalues, determinants and quadratic forms.
All Sections will use MATLAB.
MATH241
Calculus III
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141.
Credit only granted for: MATH241 or MATH340.
Introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.
All sections will use MATLAB.
MATH241H
Calculus III
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141.
Credit only granted for: MATH241 or MATH340.
Introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.
For Honors College students only. MATH 241H will use MATLAB.
MATH243
Introduction to Linear Algebra and Differential Equations
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141.
Credit only granted for: ENEE290 or MATH243.
Additional information: Does not satisfy requirements for the Mathematics or Computer Science major. Does not satisfy prerequisite requirements for courses requiring MATH240 or MATH246.
The basics of linear algebra and differential equations, with an emphasis on general physical and engineering applications. Aimed at students who need the material for future coursework but do not need as much depth and rigor as provided by MATH240 and MATH246.
MATH246
Differential Equations for Scientists and Engineers
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141.
Credit only granted for: MATH246 or MATH341.
An introduction to the basic methods of solving ordinary differential equations. Equations of first and second order, linear differential equations, Laplace transforms, numerical methods and the qualitative theory of differential equations.
All sections will use MATLAB.
MATH246H
Differential Equations for Scientists and Engineers
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141.
Credit only granted for: MATH246 or MATH341.
An introduction to the basic methods of solving ordinary differential equations. Equations of first and second order, linear differential equations, Laplace transforms, numerical methods and the qualitative theory of differential equations.
For Honors College students only. MATH 246H will use MATLAB.
MATH310
Introduction to Mathematical Proof
Credits:
3
Grad Meth:
Reg, P-F
Prerequisite: Minimum grade of C- in MATH141; and must have completed or be concurrently enrolled in MATH240, MATH341, or MATH461; and must have completed or be concurrently enrolled in MATH241 or MATH340.
Restriction: Must be in a major within the CMNS-Mathematics department; or permission of the CMNS-Mathematics department.
Additional information: Math majors may not use this course to satisfy an upper-level requirement.
To develop the students' ability to construct a rigorous proof of a mathematical claim. Students will also be made aware of mathematical results that are of interest to those wishing to analyze a particular mathematical model. Topics will be drawn from logic, set theory, structure of the number line, elementary topology, metric spaces, functions, sequences and continuity.
MATH314
Introduction to Probability, Data, Analysis and Statistics for Preservice Middle School Teachers
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH214.
Restriction: Must be in one of the following programs (Elementary Education; Special Education; Middle School Education).
Credit only granted for: MATH314 or STAT100.
Analysis of bivariate data, probability and randomness, law of large numbers, central limit theorem, probabilities for independent and dependent events, counting techniques, random variables and probability distributions, expected values, sampling distributions, and confidence intervals.
MATH341
Multivariable Calculus, Linear Algebra, Differential Equations II (Honors)
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH340.
Restriction: Open to second semester Freshmen only.
Credit only granted for: MATH240, MATH246, MATH341 or MATH461.
A continuation of MATH340.
MATH386
Experiential Learning
Credits:
3 - 6
Grad Meth:
Reg, P-F
Prerequisite: Must have learning proposal approved by the CMNS Mathematics Department.
MATH401
Applications of Linear Algebra
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH461, MATH240, MATH341).
Various applications of linear algebra: theory of finite games, linear programming, matrix methods as applied to finite Markov chains, random walk, incidence matrices, graphs and directed graphs, networks and transportation problems.
MATH402
Algebraic Structures
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH341, MATH461).
Restriction: Must not be in any of the following programs (Mathematics (Master's); Mathematics (Doctoral)).
Credit only granted for: MATH402 or MATH403.
For students having only limited experience with rigorous mathematical proofs. Parallels MATH403. Students planning graduate work in mathematics should take MATH403. Groups, rings, integral domains and fields, detailed study of several groups; properties of integers and polynomials. Emphasis is on the origin of the mathematical ideas studied and the logical structure of the subject.
MATH403
Introduction to Abstract Algebra
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH461, MATH340); and 1 course with a minimum grade of C- from (MATH341, MATH241); and minimum grade of C- in MATH310. Or students who have taken courses with comparable content may contact the department.
Credit only granted for: MATH402 or MATH403.
Integers; groups, rings, integral domains, fields.
MATH404
Field Theory
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH403.
Algebraic and transcendental elements, Galois theory, constructions with straight-edge and compass, solutions of equations of low degrees, insolubility of the quintic equation, Sylow theorems, fundamental theorem of finite Abelian groups.
MATH405
Linear Algebra
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and minimum grade of C- in MATH310.
An abstract treatment of finite dimensional vector spaces. Linear transformations and their invariants.
MATH406
Introduction to Number Theory
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH241, MATH246, MATH340, MATH341, MATH461); or permission of CMNS-Mathematics department.
Integers, divisibility, prime numbers, unique factorization, congruences, quadratic reciprocity, Diophantine equations and arithmetic functions.
MATH410
Advanced Calculus I
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241); and minimum grade of C- in MATH310.
Subjects covered: sequences and series of numbers, continuity and differentiability of real-valued functions of one variable, the Riemann integral, sequences of functions and power series.
MATH411
Advanced Calculus II
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH410; and permission of CMNS-Mathematics department.
Continuation of MATH410. Topics include: The topology of sets in Rn, the derivative matrix, the general chain rule, inverse and implicit function theorems with applications, smooth curves and surfaces in R3, Lagrange multipliers. Additional topics may include: Metric spaces, the contraction principle, the existence and uniqueness theorem for nonlinear first order differential equations, the Riemann integral of Rn, introduction to integration on curves and surfaces, Green's theorem.
MATH416
Applied Harmonic Analysis: An Introduction to Signal Processing
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141; and 1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and familiarity with MATLAB is required.
Introduces students to the mathematical concepts arising in signal analysis from the applied harmonic analysis point of view. Topics include applied linear algebra, Fourier series, discrete Fourier transform, Fourier transform, Shannon Sampling Theorem, wavelet bases, multiresolution analysis, and discrete wavelet transform.
MATH420
Mathematical Modeling
Credits:
3
Grad Meth:
Reg, P-F
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH241, MATH340); and 1 course with a minimum grade of C- from (MATH246, MATH341); and 1 course with a minimum grade of C- from (STAT400, STAT410); and 1 course with a minimum grade C- from (CMSC106, CMSC131).
Cross-listed with: AMSC420.
Credit only granted for: AMSC420 or MATH420.
The course will develop skills in data-driven mathematical modeling through individual and group projects. Emphasis will be placed on both analytical and computational methods, and on effective oral and written presentation of results.
MATH423
Linear Optimization
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH401, MATH461, or MATH341).
Credit only granted for: MATH423 or MATH498T.
Formerly: MATH498T.
Mathematical formulation of linear programming, graphical solutions, simplex method, duality, transportation problems, assignment problems, and game theory.
MATH424
Introduction to the Mathematics of Finance
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141; and 1 course with a minimum grade of C- from (STAT400, STAT410); and permission of CMNS-Mathematics department.
Recommended: MATH246, MATH240, MATH241, MATH340, or MATH341.
Credit only granted for: BMGT444, MATH424.
Introduction to the mathematical models used in finance and economics with emphasis on pricing derivative instruments. Designed for students in mathematics, computer science, engineering, finance and physics. Financial markets and instruments; elements from basic probability theory; interest rates and present value analysis; normal distribution of stock returns; option pricing; arbitrage pricing theory; the multiperiod binomial model; the Black-Scholes option pricing formula; proof of the Black-Scholes option pricing formula and applications; trading and hedging of options; Delta hedging; utility functions and portfolio theory; elementary stochastic calculus; Ito's Lemma; the Black-Scholes equation and its conversion to the heat equation.
MATH430
Euclidean and Non-Euclidean Geometries
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH341, MATH461).
Hilbert's axioms for Euclidean geometry. Neutral geometry: the consistency of the hyperbolic parallel postulate and the inconsistency of the elliptic parallel postulate with neutral geometry. Models of hyperbolic geometry. Existence and properties of isometries.
MATH437
Differential Forms
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH241, MATH340); and 1 course with a minimum grade of C- from (MATH240, MATH341, MATH461).
Recommended: MATH405, MATH403, MATH436, MATH410, or MATH432.
Introduction to differential forms and their applications, and unites the fundamental theorems of multivariable calculus in a general Stokes Theorem that is valid in great generality. It develops this theory and technique to perform calculations in analysis and geometry. Topics include an introduction to topological spaces, the Gauss-Bonnet Theorem, Gauss's formula for the linking number, and the Cauchy Integral Theorem. Applications include Maxwell's equations of electromagnetism, connections and gauge theory, and symplectic geometry and Hamiltonian dynamics.
MATH446
Axiomatic Set Theory
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH403, MATH410).
Development of a system of axiomatic set theory, choice principles, induction principles, ordinal arithmetic including discussion of cancellation laws, divisibility, canonical expansions, cardinal arithmetic including connections with the axiom of choice, Hartog's theorem, Konig's theorem, properties of regular, singular and inaccessible cardinals.
MATH452
Introduction to Dynamics and Chaos
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH341; or MATH246 and one of (MATH240 or MATH461).
Cross-listed with: AMSC452.
Credit only granted for: AMSC452 or MATH452.
An introduction to mathematical dynamics and chaos. Orbits, bifurcations, Cantor sets and horseshoes, symbolic dynamics, fractal dimension, notions of stability, flows and chaos. Includes motivation and historical perspectives, as well as examples of fundamental maps studied in dynamics and applications of dynamics.
MATH456
Cryptography
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: (CMSC106, CMSC131, or ENEE150; or equivalent programming experience); and (2 courses from (CMSC330, CMSC351, ENEE324, or ENEE380); or any one of these courses and a 400-level MATH course, or two 400-level MATH courses); and Permission of CMNS-Mathematics department or permission of instructor.
Cross-listed with: CMSC456, ENEE456.
Credit only granted for: MATH456, CMSC456 or ENEE456.
The theory, application, and implementation of mathematical techniques used to secure modern communications. Topics include symmetric and public-key encryption, message integrity, hash functions, block-cipher design and analysis, number theory, and digital signatures.
MATH461
Linear Algebra for Scientists and Engineers
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141; and must have completed a MATH or STAT course with a prerequisite of MATH141.
Credit only granted for: MATH240, MATH341, or MATH461.
Additional information: This course may not be used towards the upper level math requirements for MATH/STAT majors.
Basic concepts of linear algebra. This course is similar to MATH240, but with more extensive coverage of the topics needed in applied linear algebra: change of basis, complex eigenvalues, diagonalization, the Jordan canonical form.
All Sections will use MATLAB.
MATH462
Partial Differential Equations
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH241, MATH340); and 1 course with a minimum grade of C- from (MATH246, MATH341).
Linear spaces and operators, orthogonality, Sturm-Liouville problems and eigenfunction expansions for ordinary differential equations. Introduction to partial differential equations, including the heat equation, wave equation and Laplace's equation. Boundary value problems, initial value problems and initial-boundary value problems.
MATH463
Complex Variables
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH241, MATH340).
The algebra of complex numbers, analytic functions, mapping properties of the elementary functions. Cauchy integral formula. Theory of residues and application to evaluation of integrals. Conformal mapping.
MATH464
Transform Methods
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH246, MATH341).
Fourier transform, Fourier series, discrete fast Fourier transform (DFT and FFT). Laplace transform. Poisson summations, and sampling. Optional Topics: Distributions and operational calculus, PDEs, Wavelet transform, Radon transform and applications such as Imaging, Speech Processing, PDEs of Mathematical Physics, Communications, Inverse Problems.
MATH470
Mathematics for Secondary Education
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH141 and MATH140; and must have completed one 400-level MATH course (not to include MATH461, 478, and 480's).
Restriction: Must be in the Secondary Math Education major.
An advanced perspective on some of the core mathematics underlying high school mathematics courses. Topics include number systems, functions of one variable, equations, inequalities, trigonometric functions, curve fitting, and polynomials. The course includes an analysis of alternate approaches to mathematical ideas and problems, and makes connections between ideas that may have been studied separately in different high school and college courses.
MATH475
Combinatorics and Graph Theory
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH240, MATH341, MATH461); and 1 course with a minimum grade of C- from (MATH241, MATH340); and permission of CMNS-Mathematics department.
Cross-listed with CMSC475.
Credit only granted for: MATH475 or CMSC475.
General enumeration methods, difference equations, generating functions. Elements of graph theory, matrix representations of graphs, applications of graph theory to transport networks, matching theory and graphical algorithms.
MATH489
Research Interactions in Mathematics; Research Interactions in Mathematics
Credits:
1 - 3
Grad Meth:
Reg, P-F, Aud
MATH498A
Selected Topics in Mathematics
Credits:
1 - 9
Grad Meth:
Reg, P-F, Aud
MATH601
Abstract Algebra II
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH600.
Field theory, Galois theory, multilinear algebra. Further topics from: Dedekind domains, Noetherian domains, rings with minimum condition, homological algebra.
Offered Spring only.
MATH603
Commutative Algebra
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: MATH600.
Ideal theory of Noetherian rings, valuations, localizations, complete local rings, Dedekind domains.
MATH607
Algebraic Geometry II
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: MATH606.
Topics in contemporary algebraic geometry chosen from among: theory of algebraic curves and surfaces, elliptic curves, Abelian varieties, theory of schemes, theory of zeta functions, formal cohomology, algebraic groups, reduction theory.
MATH621
Algebraic Number Theory II
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: MATH600. And MATH620; or students who have taken courses with comparable content may contact the department.
Valuation of a field, algebraic function fields, completion of a valuation field, ramification exponent and residue class degree, ramification theory, elements, differents, discriminants, product formula and characterization of fields by the formula, Gauss sum, class number formula of cyclotomic fields.
MATH631
Real Analysis II
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH630.
Abstract measure and integration theory, metric spaces, Baire category theorem and uniform boundedness principle, Radon-Nikodym theorem, Riesz Representation theorem, Lebesgue decomposition, Banach and Hilbert Spaces, Banach-Steinhaus theorem, topological spaces, Arzela-Ascoli and Stone-Weierstrass theorems, compact sets and Tychonoff's theorem.
Offered Spring only.
MATH660
Complex Analysis I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH410 and MATH463; or students who have taken courses with comparable content may contact the department.
Linear transformations, analytic functions, conformal mappings, Cauchy's theorem and applications, power series, partial fractions and factorization, elementary Riemann surfaces, Riemann's mapping theorem.
MATH674
Partial Differential Equations II
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH673 or AMSC673; or permission of instructor.
Cross-listed with: AMSC674.
Credit only granted for: AMSC674 or MATH674.
Boundary value problems for elliptic partial differential equations via operator-theoretic methods. Hilbert spaces of functions. Duality, weak convergence. Sobolev spaces. Spectral theory of compact operators. Eigenfunction expansions.
Offered Spring only.
MATH675
Analysis and PDEs
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH630 or MATH674; or permission of instructor.
Introduction to tools of modern analysis which have been used in recent years in the study of partial differential equations: Fourier transform, Calderon-Zygmund theory, interpolation, Lebesgue spaces, Lorentz spaces, Sobolev spaces, Besov spaces, Littlewood-Paley theory, multipliers, Bernstein inequalities, the fractional Leibniz rule, Strichartz estimates, velocity averaging lemma. Applications to some of the following PDEs: the Navier-Stokes equations, Euler equations, nonlinear Schrodinger equations, nonlinear wave equations, the Patlak Keller Segel model.
MATH689
Research Interactions in Mathematics
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH713
Mathematical Logic II
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH712.
Incompleteness and undecidability results of Godel, Church, Tarski and others. Recursive function. Basic proof theory and axiomatic set theory.
MATH734
Algebraic Topology
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH600; and MATH432 or MATH730; or students who have taken courses with comparable content may contact the department.
Singular homology and cohomology, cup products, Poincare duality, Eilenberg-Steenrod axioms, Whitehead and Hurewicz theorems, universal coefficient theorem, cellular homology.
MATH740
Fundamental Concepts of Differential Geometry
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH405, MATH411, and MATH730; or students who have taken courses with comparable content may contact the department.
Manifolds, tangent vectors and differential forms, Riemannian metrics, connections, curvature, structure equations, geodesics, calculus of variations.
MATH744
Lie Groups I
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: MATH405, MATH403, MATH411, and MATH432; or students who have taken courses with comparable content may contact the department.
An introduction to the fundamentals of Lie groups, including some material on groups of matrices and Lie algebras.
MATH799
Master's Thesis Research
Credits:
1 - 6
Grad Meth:
S-F
MATH808A
Selected Topics in Algebra
Credits:
1 - 3
Grad Meth:
Reg
MATH818A
Selected Topics in Logic
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH818T
Selected Topics in Logic; Recent Development in Model Theory
Credits:
1 - 3
Grad Meth:
Reg, Aud, S-F
MATH838B
Topics in Dynamics; Introduction to KAM theory
Credits:
1 - 3
Grad Meth:
Reg
MATH838R
Topics in Dynamics; Lyapunov Exponents
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH848A
Selected Topics in Geometry and Topology
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH848G
Selected Topics in Geometry and Topology; Characteristic Classes of G-Bundles
Credits:
1 - 3
Grad Meth:
Reg, Aud, S-F
MATH848Z
Selected Topics in Geometry and Topology; Topology of 4-Manifolds
Credits:
1 - 3
Grad Meth:
Reg, Aud, S-F
MATH858A
Selected Topics in Analysis
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH858M
Selected Topics in Analysis; Stochastic Methods with Applications
Credits:
1 - 3
Grad Meth:
Reg, Aud, S-F
MATH858R
Selected Topics in Analysis; Ramsey Theory and its Applications
Credits:
3
Grad Meth:
Reg, Aud
Cross-listed with CMSC752. Credit only granted for CMSC752, CMSC858R, or MATH858R.
MATH868A
SelectedTopics in Complex Analysis
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH868B
SelectedTopics in Complex Analysis; Selected Topics in Complex Variables
Credits:
1 - 3
Grad Meth:
Reg, Aud, S-F
MATH898
Pre-Candidacy Research
Credits:
1 - 8
Grad Meth:
Reg
MATH899
Doctoral Dissertation Research
Credits:
6
Grad Meth:
S-F
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