Courses - Fall 2024
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.
There is a special fee for this class in addition to the regular tuition charge.
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.
There is a special fee for this class in addition to the regular tuition charge.
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.
There is a special fee for this class in addition to the regular tuition charge.
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.
There is a special fee for this class in addition to the regular tuition charge.
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.
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.
Preparation for MATH120, MATH135 or MATH140. Elementary functions and graphs: polynomials, rational functions, exponential and logarithmic functions, trigonometric functions. Algebraic techniques preparatory for calculus.
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.
MATH140H
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.
For general honors students only. Offered fall only.
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.
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, 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, 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, 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.
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 general honors students only. MATH241H 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 general honors students only. MATH241H will use MATLAB.
MATH274
History of Mathematics
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH120, MATH130, MATH136, or MATH140; or must have completed MATH220.
An overview of aspects in the history of mathematics from its beginning in the concrete problem solving of ancient times through the development of abstraction in the 19th and 20th centuries. The course considers both mathematical ideas and the context in which they developed in various civilizations around the world.
MATH299B
Selected Topics in Mathematics; Putnam Express
Credits:
1
Grad Meth:
Reg, P-F, Aud
MATH310
Introduction to Mathematical Proof
Credits:
3
Grad Meth:
Reg
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.
MATH312
Mathematical Reasoning and Proof for Pre-Service Middle School Teachers
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH212 and MATH213.
Restriction: Must be in one of the following programs (Elementary Education; Special Education; Middle School Education).
Reasoning and proof as addressed in the middle school curriculum. Topics include proportional reasoning, logic and proof, types of numbers, field axioms, Euclidean and non-Euclidean geometry.
MATH315
Algebra for Preservice Middle School Teachers
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH212.
Restriction: Must be in one of the following programs (Elementary Education; Special Education; Middle School Education).
Credit only granted for: MATH113 or MATH315.
Algebraic concepts and techniques developed in the middle grades, with their larger mathematical context. Equations, inequalities and functions (linear, polynomial, exponential, logarithmic), with multiple representations of relationships. Common misconceptions of beginning algebra students.
MATH340
Multivariable Calculus, Linear Algebra and Differential Equations I (Honors)
Credits:
4
Grad Meth:
Reg, P-F, Aud
Prerequisite: MATH141 and MATH140; and permission of CMNS-Mathematics department; and permission will be granted only to incoming freshmen.
Credit only granted for: MATH241 or MATH340.
First semester of the MATH340-341 sequence which gives a unified and enriched treatment of multivariable calculus, linear algebra and ordinary differential equations, with supplementary material from subjects such as differential geometry, Fourier series and calculus of variations. Students completing MATH340-341 will have covered the material of MATH240, MATH241, and MATH246, and may not also receive credit for MATH240, MATH241 or MATH246.
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.
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.
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.
MATH431
Geometry for Computer Applications
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: 1 course with a minimum grade of C- from (MATH461, MATH240, MATH341).
Topics from projective geometry and transformation geometry, emphasizing the two-dimensional representation of three-dimensional objects and objects moving about in the plane and space. The emphasis will be on formulas and algorithms of immediate use in computer graphics.
MATH432
Introduction to Topology
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH410.
Metric spaces, topological spaces, connectedness, compactness (including Heine-Borel and Bolzano-Weierstrass theorems), Cantor sets, continuous maps and homeomorphisms, fundamental group (homotopy, covering spaces, the fundamental theorem of algebra, Brouwer fixed point theorem), surfaces (e.g., Euler characteristic, the index of a vector field, hairy sphere theorem), elements of combinatorial topology (graphs and trees, planarity, coloring problems).
MATH436
Differential Geometry of Curves and Surfaces I
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 (MATH461, MATH240, MATH341); and must have completed two 400-level MATH courses with a minimum grade of C- (not including MATH461, and 480's).
Curves in the plane and Euclidean space, moving frames, surfaces in Euclidean space, orientability of surfaces; Gaussian and mean curvatures; surfaces of revolution, ruled surfaces, minimal surfaces, special curves on surfaces, "Theorema Egregium"; the intrinsic geometry of surfaces.
MATH445
Elementary Mathematical Logic
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Minimum grade of C- in MATH141.
Elementary development of propositional and predicate logic, including semantics and deductive systems and with a discussion of completeness, incompleteness and the decision problem.
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.
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.
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.
MATH487
Number for Middle Grades Teachers
Credits:
3
Grad Meth:
Reg, P-F, Aud
Prerequisite: Must have admission to M.A. or M.Ed. with concentration in Mathematics Education; or permission of CMNS-Mathematics department.
Restriction: This course may not be used towards the upper level math requirements for the MATH/STAT major.
Credit only granted for: MATH487 or MATH498K.
Formerly: MATH498K.
The rational number and proportional reasoning concepts developed in the middle grades and the larger mathematical context for these. Multiple representations of relationships, including verbal descriptions, diagrams, tables, graphs, and equations. Common misconceptions.
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
MATH600
Abstract Algebra I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH405 and MATH403; or students who have taken courses with comparable content may contact the department.
Groups with operators, homomorphism and isomorphism theorems, normal series, Sylow theorems, free groups, Abelian groups, rings, integral domains, fields, modules. Topics may include HOM (A,B), Tensor products, exterior algebra.
Offered fall only.
MATH606
Algebraic Geometry I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH600 and MATH601.
Prime and primary ideals in Noetherian rings, Hilbert Nullstellensatz, places and valuations, prevarieties (in the sense of Serre), dimension, morphisms, singularities, varieties, schemes, rationality.
MATH620
Algebraic Number Theory I
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: MATH601.
Algebraic numbers and algebraic integers, algebraic number fields of finite degree, ideals and units, fundamental theorem of algebraic number theory, theory of residue classes, Minkowski's theorem on linear forms, class numbers, Dirichlet's theorem on units, relative algebraic number fields, decomposition group, inertia group and ramification group of prime ideals with respect to a relatively Galois extension.
MATH630
Real Analysis I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH411; or students who have taken courses with comparable content may contact the department.
Lebesgue measure and the Lebesgue integral on R, differentiation of functions of bounded variation, absolute continuity and fundamental theorem of calculus, Lp spaces on R, Riesz-Fischer theorem, bounded linear functionals on Lp, measure and outer measure, Fubini's theorem.
MATH632
Functional Analysis
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: MATH631.
Introduction to functional analysis and operator theory: normed linear spaces, basic principles of functional analysis, bounded linear operators on Hilbert spaces, spectral theory of selfadjoint operators, applications to differential and integral equations, additional topics as time permits.
MATH636
Representation Theory
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: MATH631.
Introduction to representation theory of Lie groups and Lie algebras; initiation into non-abelian harmonic analysis through a detailed study of the most basic examples, such as unitary and orthogonal groups, the Heisenberg group, Euclidean motion groups, the special linear group. Additional topics from the theory of nilpotent Lie groups, semisimple Lie groups, p-adic groups or C-algebras.
MATH642
Dynamical Systems I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH432. And MATH630; or students who have taken courses with comparable content may contact the department.
Foundations of topological dynamics, homeomorphisms, flows, periodic and recurrent points, transitivity and minimality, symbolic dynamics. Elements of ergodic theory, invariant measures and sets, ergodicity, ergodic theorems, mixing, spectral theory, flows and sections. Applications of dynamical systems to number theory, the Weyl theorem, the distribution of values of polynomials, Vander Waerden's theorem on arithmetic progressions.
MATH661
Complex Analysis II
Credits:
3
Grad Meth:
Reg, Aud, S-F
Prerequisite: MATH630 and MATH660.
Introduction to techniques of several complex variables, with focus on geometric topics: Hartogs phenomena, Cousin problems, Dolbeault cohomology, L2 techniques, embedding of Stein manifolds, and the theory of coherent analytic sheaves.
MATH673
Partial Differential Equations I
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH411; or students who have taken courses with comparable content may contact the department.
Cross-listed with: AMSC673.
Credit only granted for: AMSC673 or MATH673.
Analysis of boundary value problems for Laplace's equation, initial value problems for the heat and wave equations. Fundamental solutions, maximum principles, energy methods. First order nonlinear PDE, conservation laws. Characteristics, shock formation, weak solutions. Distributions, Fourier transform.
Offered fall only.
MATH689
Research Interactions in Mathematics
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH695
Teaching Seminar
Credits:
1
Grad Meth:
Reg
Restriction: Must be in one of the following programs (Mathematics (Doctoral); Mathematics (Master's); Mathematical Statistics (Doctoral); Applied Mathematics and Scientific Computation (Master's); Mathematical Statistics (Master's); Applied Mathematics and Scientific Computation (Doctoral)).
A course intended for first year teaching assistants. Topics include: everyday mechanics of teaching; teaching methods and styles; technology; course enrichment, diversity in the classroom; sexual harassment; teacher-student interactions; presentations by students.
MATH712
Mathematical Logic I
Credits:
3
Grad Meth:
Reg, Aud
Sentential logic, first-order languages, models and formal deductions. Basic model theory including completeness and compactness theorems, other methods of constructing models, and applications such as non-standard analysis.
MATH730
Fundamental Concepts of Topology
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH403, MATH410, and MATH411; or students who have taken courses with comparable content may contact the department.
Survey of basic point set topology, fundamental group, covering spaces, Van Kampen's theorem, simplicial complexes, simplicial homology, Euler characteristics and classification of surfaces.
MATH742
Geometric Analysis
Credits:
3
Grad Meth:
Reg, Aud
Prerequisite: MATH673 and MATH674; or MATH740.
Calculus of Variations, Bochner technique, Morse theory, weak solutions and elliptic regularity, maximum principle for elliptic and parabolic equations, Green's function of the Laplacian, isoperimetric and Sobolev inequalities, continuity method, curvature and comparison results, harmonic maps, curvature prescription problems.
MATH799
Master's Thesis Research
Credits:
1 - 6
Grad Meth:
S-F
MATH808A
Selected Topics in Algebra
Credits:
1 - 3
Grad Meth:
Reg
MATH808E
Selected Topics in Algebra; Complex abelian varieties
Credits:
3
Grad Meth:
Reg, Aud, S-F
MATH818A
Selected Topics in Logic
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH818C
Selected Topics in Logic; Descriptive Set Theory and Abstract Analysis
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH838C
Topics in Dynamics
Credits:
1 - 3
Grad Meth:
Reg
MATH848A
Selected Topics in Geometry and Topology
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH848N
Selected Topics in Geometry and Topology; Topics in Differential Geometry
Credits:
1 - 3
Grad Meth:
Reg, Aud, S-F
MATH858A
Selected Topics in Analysis
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH858C
Selected Topics in Analysis; Mathematical Methods in Machine Learning
Credits:
1 - 3
Grad Meth:
Reg, Aud, S-F
MATH858F
Selected Topics in Analysis; Collective Dynamics of Active Particles
Credits:
1 - 3
Grad Meth:
Reg, Aud, S-F
Ants form colonies, birds flock, mobile networks synchronize, and a consensus may emerge from the interaction of diverse human opinions. These are simple examples of collective dynamics in which small-scale interactions lead to the emergence of larger-scale patterns.
We will survey recent mathematical developments in collective dynamics. Three levels of descriptions are considered: agent-based dynamics on graphs, Vlasov-type kinetic description, and large-crowd hydrodynamics. The dynamics is governed by different protocols of pairwise interactions. Different models for such protocols of attraction, alignment, and repulsion go back to the influential works of Reynolds, Krause, Vicsek, and Cucker & Smale.
We will survey recent mathematical developments in collective dynamics. Three levels of descriptions are considered: agent-based dynamics on graphs, Vlasov-type kinetic description, and large-crowd hydrodynamics. The dynamics is governed by different protocols of pairwise interactions. Different models for such protocols of attraction, alignment, and repulsion go back to the influential works of Reynolds, Krause, Vicsek, and Cucker & Smale.
Click for more course information.
MATH858I
Selected Topics in Analysis; Reaction - Diffusion Equations
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH868A
SelectedTopics in Complex Analysis
Credits:
1 - 3
Grad Meth:
Reg, Aud
MATH898
Pre-Candidacy Research
Credits:
1 - 8
Grad Meth:
Reg
MATH899
Doctoral Dissertation Research
Credits:
6
Grad Meth:
S-F
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