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Materials Science Courses numbered X37; X97; 300, 400 are described in the University Academic Policies section of this catalog. |
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MSCI 201 - Introduction to Engineering Materials
The relationship between the properties, structure and processes of engineering materials is discussed. Emphasis on the fundamentals of selecting materials based on engineering design criteria. Also offered as ETEC 220.
Prerequisites & Notes:
CHEM 121 or CHEM 125; MATH 115 or MATH 118; PHYS 161 or concurrent.
Credits: 4
Grade Mode: Letter
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MSCI 320 - Introduction to Materials Science I
The first course in a three course interdisciplinary sequence designed to cover the fundamental concepts of materials science. Basic atomic structures, basic organic and polymer chemistry, synthesis of organic materials, polymers, composites, and basic characterization methods are covered in this first overview course. ETEC majors may substitute ETEC 333 + 334 + CHEM 251 for MSCI 320.
Prerequisites & Notes:
CHEM 123 or CHEM 225.
Credits: 4
Grade Mode: Letter
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MSCI 330 - Introduction to Materials Science II
The second course in a three course interdisciplinary sequence designed to cover the fundamental concepts of materials science. Electrical, magnetic and optical properties and structures of materials are emphasized in this second overview course. ETEC majors may substitute ETEC 333 + 334 + CHEM 251 for MSCI 320.
Prerequisites & Notes:
MATH 125 or MATH 135 or MATH 138; PHYS 161, PHYS 162, PHYS 163; MSCI 320
Credits: 4
Grade Mode: Letter
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MSCI 410 - Characterization of Materials
The third course in a three course interdisciplinary sequence designed to cover the fundamental concepts of materials science. Theory and operating principals of external and internal characterization of materials such as: electron microscopy, x-ray chemical microanalysis, optical microscopy, thermal, magnetic and structural analysis, polymer processing and analysis, thin film preparation and characterization, and x-ray diffraction. Laboratory experience and projects are emphasized.
Prerequisites & Notes:
MSCI 330 or CHEM 461 or GEOL 306
Credits: 4
Grade Mode: Letter
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MSCI 491 - Independent Research or Internship in Materials Science I
Undergraduate research in materials science or an undergraduate internship in materials science in industry under supervision.
Prerequisites & Notes:
MSCI 330.
Credits: 3
Grade Mode: Letter
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MSCI 492 - Independent Research or Internship in Materials Science II
Undergraduate research in materials science or an undergraduate internship in materials science in industry under supervision.
Prerequisites & Notes:
MSCI 330.
Credits: 3
Grade Mode: Letter
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Mathematics Courses numbered X37; X97; 300, 400, 500 are described in the University Academic Policies section of this catalog. |
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MATH 099 - Introductory Algebra
Gain skill working with algebraic language and concepts using graphs, tables and algebraic expressions and equations in order to prepare for math 112. Develop problem solving abilities and understanding. Polynomials, exponents, roots, radicals, and linear equations and inequalities and their graphs. Pass/Fail grading.
Prerequisites & Notes:
NOTE: This course will fulfill 5 credits towards financial aid and veterans benefits requirements only. No credit will be allowed toward the graduation requirement of 180 credits.
Credits: 5
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MATH 101 - Functions and Algebraic Methods for K-8 Teachers
Designed for prospective K-8 teachers. Emphasizes pattern recognition and generalization, building mathematical models and problem solving. Supporting topics include polynomials, linear and quadratic equations, inequalities, graphs, rational expressions and functions. Graphing calculators required. Cannot be counted toward majors or minors in mathematics or computer science.
Prerequisites & Notes:
Suitable General Math Placement Test score or college intermediate algebra course with a C- or better; instructor permission.
Credits: 5
Grade Mode: Letter
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MATH 106 - Quantitative Reasoning
Develops abilities to understand quantitative information and make reasoned decisions using it. Focus is on reasoning and symbolic and quantitative models as they are commonly encountered in personal life, careers and public issues.
Credits: 4
Grade Mode: Letter
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MATH 107 - Mathematical Reasoning and Its Applications
Reading quantitative information, reasoning, personal finance, data display and summary, assessing risk; quantitative decisions in life, careers, and public issues. Students interested in taking higher level mathematics courses should instead take a course from MATH 112, 114, 118, 124, 156, 157 or 240. Note: This course is not an acceptable prereq for MATH 112.
Prerequisites & Notes:
Suitable General Math Placement Test score or C- or better in MATH 112 or MATH 106, or college intermediate algebra course.
Credits: 4
Grade Mode: Letter
GUR Attributes: QSR
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MATH 112 - Functions and Algebraic Methods
Pattern recognition and generalization, building mathematical models and problem solving are emphasized. Supporting topics include polynomials, linear and quadratic equations, inequalities, graphs, rational expressions, radicals and functions. Graphing calculator required. Cannot be counted toward majors or minors in mathematics or computer science.
Prerequisites & Notes:
Suitable General Math Placement Test score, MATH 99 or completion of a college intermediate algebra course with a C- or better. Note: Neither MATH 106 nor MATH 107 is acceptable pre-requisite for this course.
Credits: 5
Grade Mode: Letter
GUR Attributes: QSR
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MATH 114 - Precalculus I
Data analysis, functions as mathematical models, functions and their graphs. Graphing calculators are required. Cannot be counted toward majors or minors in mathematics or computer science. Students needing math for GUR purposes only should consider MATH 107 instead of MATH 114.
Prerequisites & Notes:
Suitable General Math Placement Test score or MATH 112 with a C- or better.
Credits: 5
Grade Mode: Letter
GUR Attributes: QSR
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MATH 115 - Precalculus II
Data analysis, modeling, trigonometry, inverse functions. Graphing calculator required. Cannot be counted toward majors or minors in mathematics or computer science.
Prerequisites & Notes:
MATH 114 with a C- or better at Western
Credits: 5
Grade Mode: Letter
GUR Attributes: QSR
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MATH 118 - Accelerated Precalculus
Not open to students who have taken a lower numbered mathematics course at Western. Functions as mathematical models, functions and their graphs, inverse functions, trigonometry. Graphing calculator required. Cannot be counted toward majors or minors in mathematics or computer science.
Prerequisites & Notes:
Suitable General or Advanced Math Placement Test score
Credits: 5
Grade Mode: Letter
GUR Attributes: QSR
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MATH 119A - Topics in Mathematics
A supplement to one or more math courses offered at the 100 level. Repeatable, subject to permission of department.
Prerequisites & Notes:
Permission of instructor.
Credits: 1-15
Grade Mode: Letter
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MATH 119B - Topics in Mathematics
A supplement to one or more math courses offered at the 100 level. Repeatable, subject to permission of department. S/U grading.
Prerequisites & Notes:
Permission on instructor.
Credits: 1-15
Grade Mode: S/U
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MATH 124 - Calculus and Analytic Geometry I
Average and instantaneous rates of change, interpretation, computation, and application of derivatives to optimization, rates, graphing, and antiderivative problems. Graphing calculator required.
Prerequisites & Notes:
Suitable Advanced Math Placement Test score or C- or better in MATH 115 or MATH 118 at WWU or a grade of 2.5 or higher in the final quarter of a college precalculus sequence.
Credits: 5
Grade Mode: Letter
GUR Attributes: QSR
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MATH 125 - Calculus and Analytic Geometry II
The definite integral, techniques of integration, applications including area and volume, growth and decay, introduction to differential equations.
Prerequisites & Notes:
MATH 124 or MATH 134.
Credits: 5
Grade Mode: Letter
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MATH 134 - Calculus I Honors
Intended for particularly strong students. Average and instantaneous rates of change, interpretation, computation, and application of derivatives to optimization, rates, graphing, and antiderivative problems. Frequent writing assignments. Graphing calculator required.
Prerequisites & Notes:
Suitable score on the Advanced Mathematics Placement test or an A in MATH 115 or MATH 118, and permission of instructor.
Credits: 5
Grade Mode: Letter
GUR Attributes: QSR
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MATH 135 - Calculus II Honors
Intended for particularly strong students. Riemann sums and the definite integral, interpretation and application to area, volume, growth and decay, techniques of integration. Introduction to differential equations. Frequent writing assignments.
Prerequisites & Notes:
MATH 124 or MATH 134, and permission of instructor.
Credits: 5
Grade Mode: Letter
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MATH 138 - Accelerated Calculus
Designed for entering freshmen who are thoroughly familiar with the computational aspects of single variable calculus. Students study selected topics from MATH 124 and 125 from a more conceptual point of view. Students who complete this course receive five credits of advanced placement (unless previously received). Not open to students who have taken MATH 124 or 125. Offered fall quarter only. AP mathematics credit and MATH 138 are equivalent to MATH 124 and 125.
Prerequisites & Notes:
One year AP-level High School calculus; suitable score on the Advanced Math Placement Test and permission of instructor.
Credits: 5
Grade Mode: Letter
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MATH 156 - Algebra With Applications to Business and Economics
Equations and inequalities, graphs and functions, exponential and logarithmic functions, applications to finance. This course is designed for business students continuing on to MATH 157.
Prerequisites & Notes:
Suitable General Math Placement Test score or MATH 112 with a C- or better.
Credits: 4
Grade Mode: Letter
GUR Attributes: QSR
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MATH 157 - Calculus With Applications to Business and Economics
Limits, rates of change, differentiation, graphing and optimization, integration, business applications, partial differentiation. MATH 124 may be substituted for MATH 157 but not vice versa. Cannot be taken for credit by a student who has already completed another college-level calculus course.
Prerequisites & Notes:
Suitable Advanced Math Placement Test score or C- or better in MATH 156, MATH 114 or MATH 118; or a final precalculus course with a C+ or better from an accredited college.
Credits: 4
Grade Mode: Letter
GUR Attributes: QSR
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MATH 203 - Linear Algebra and Differential Equations I
First course in the 203-303 sequence. A unified treatment of the material on elementary linear algebra and elementary differential equations covered in MATH 204 and 331. Together with MATH 303, is equivalent to MATH 204 and MATH 331.
Prerequisites & Notes:
MATH 125 or MATH 135 or equivalent
Credits: 4
Grade Mode: Letter
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MATH 204 - Elementary Linear Algebra
Systems of linear equations; matrices; the vector space Rn; linear independence, bases, subspaces and dimension in Rn; introduction to determinants and the eigenvalue problem; applications.
Prerequisites & Notes:
MATH 125 or MATH 135; MATH 224 recommended
Credits: 4
Grade Mode: Letter
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MATH 205 - Linear Algebra Workshop
Elementary linear algebra projects on a computer. S/U grading.
Prerequisites & Notes:
Math 204 or concurrent.
Credits: 1
Grade Mode: S/U
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MATH 220 - Visualization in Multivariable Calculus
Weekly lab projects emphasizing the creation and interpretation of computer-generated graphs and contour diagrams for functions of several variables. Problems are drawn from material being studied in MATH 224. S/U grading.
Prerequisites & Notes:
Math 224 or concurrent.
Credits: 1
Grade Mode: S/U
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MATH 224 - Multivariable Calculus and Geometry I
Coordinate systems, curves and vectors in the plane and in space, partial derivatives, applications including optimization and motion, multiple integrals.
Prerequisites & Notes:
MATH 125 or MATH 135, or MATH 138
Credits: 5
Grade Mode: Letter
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MATH 225 - Multivariable Calculus and Geometry II
Multiple integrals, line and surface integrals, gradient fields, Green’s and Stokes’ theorems.
Prerequisites & Notes:
MATH 224
Credits: 4
Grade Mode: Letter
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MATH 226 - Limits and Infinite Series
Formal treatment of limits of functions and sequences of continuity, including a thorough training in constructing rigorous proofs of the epsilon-delta type. Convergence tests for infinite series. Radius of convergence, differentiation, and integration of Taylor series.
Prerequisites & Notes:
MATH 125, MATH 135 or MATH 138
Credits: 4
Grade Mode: Letter
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MATH 240 - Introduction to Statistics
Descriptive statistics, basic ideas of probability, normal distribution, sampling distributions, confidence intervals, hypothesis testing, contingency tables, and one-way analysis of variance. Use of a statistical software package. Cannot be counted toward any major in the Department of Mathematics.
Prerequisites & Notes:
Suitable General Math Placement Test score or MATH 112 or a precalculus course with a C+ or better from an accredited college.
Credits: 4
Grade Mode: Letter
GUR Attributes: QSR
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MATH 245 - Statistics for Engineering Technology
Descriptive statistics, basic probability, discrete distributions, normal distribution, statistical methods used in engineering.
Prerequisites & Notes:
MATH 115 or MATH 118.
Credits: 3
Grade Mode: Letter
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MATH 302 - Introduction to Proofs Via Number Theory
The properties of integers, prime numbers, Euclidean algorithm, congruences. The student is expected to develop competence in proving basic results in number theory.
Prerequisites & Notes:
MATH 125 or MATH 135 or MATH 138
Credits: 4
Grade Mode: Letter
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MATH 303 - Linear Algebra and Differential Equations II
Second course in the MATH 203-303 sequence. A unified treatment of the material on elementary linear algebra and elementary differential equations covered in MATH 204 and 331. Together with MATH 203, is equivalent to MATH 204 and MATH 331.
Prerequisites & Notes:
MATH 203
Credits: 4
Grade Mode: Letter
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MATH 304 - Linear Algebra
Orthogonality and orthogonal bases; linear transformations and the least squares problem; further study of eigenvalues and eigenvectors and their applications; abstract vector spaces and linear transformations.
Prerequisites & Notes:
MATH 204, MATH 224
Credits: 4
Grade Mode: Letter
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MATH 307 - Mathematical Computing
Use of mathematical software such as Matlab and Mathematica. Elementary programming, numerical and symbolic computation, visualization and technical reporting in mathematical context.
Prerequisites & Notes:
MATH 125 or MATH 135 or MATH 138; MATH 204
Credits: 4
Grade Mode: Letter
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MATH 309 - Introduction to Proof in Discrete Mathematics
Logic, sets, functions, sequences, counting methods, graph theory. The student is expected to develop competence in proving basic results in discrete mathematics.
Prerequisites & Notes:
MATH 125
Credits: 4
Grade Mode: Letter
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MATH 312 - Proofs in Elementary Analysis
Open and closed sets in the line and plane, sequences, least upper bound axiom, continuous functions and their properties. The student is expected to develop competence in proving basic theorems involving these concepts.
Prerequisites & Notes:
MATH 226; MATH 302 or MATH 309. Restricted to majors and minors during Registration Phase 1.
Credits: 4
Grade Mode: Letter
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MATH 321 - Mathematics for Technology
A survey of topics from differential equations and the Laplace Transform. Designed especially for students majoring in engineering technology. Students may count only one of MATH 321 or MATH 331 toward any major or minor in the Department of Mathematics.
Prerequisites & Notes:
MATH 125 or MATH 135
Credits: 4
Grade Mode: Letter
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MATH 331 - Ordinary Differential Equations
First order equations, first order systems (primarily linear), applications and modeling, qualitative reasoning. First course in the 331-432 sequence.
Prerequisites & Notes:
Math 204; Math 224 recommended or concurrent.
Credits: 4
Grade Mode: Letter
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MATH 341 - Probability and Statistical Inference
Probability, including combinatorial methods, discrete distributions and continuous distributions using integrals. Descriptive statistics and the use of computer statistical package. Statistical inference, including confidence intervals and hypothesis testing.
Prerequisites & Notes:
MATH 125 or MATH 135 or MATH 138
Credits: 4
Grade Mode: Letter
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MATH 342 - Statistical Methods
Statistical techniques including chi-square tests, simple and multiple linear regression, and one-way analysis of variance. Extensive use of a computer statistical package.
Prerequisites & Notes:
MATH 341
Credits: 4
Grade Mode: Letter
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MATH 360 - Euclidean and Non-Euclidean Geometry
Metric development of Euclidean geometry and consideration of non-Euclidean geometries.
Prerequisites & Notes:
MATH 125 or MATH 135 or MATH 138; MATH 204 and MATH 302 or MATH 309.
Credits: 4
Grade Mode: Letter
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MATH 381 - Teaching K-8 Mathematics I
Investigations of mathematics topics that focus on logical reasoning, number concepts, and number operations. Emphasis on problem solving, the use of manipulatives and computing technologies, remediation and resource materials, and optimal pedagogical techniques that help students learn quality mathematics. Not acceptable for any departmental major except BA/Ed, Elementary, and does not satisfy GUR requirement except for those who complete the BA/Ed, Elementary.
Prerequisites & Notes:
Suitable Intermediate Math Placement Test score; C or better in MATH 112 or college intermediate algebra course; one of ELED 370, ELED 372, SPED 420, ECE 391; Prerequisites must have been met within the last 5 years. Waiver of MPT due to college calculus course equivalent to WWU MATH 124.
Credits: 4
Grade Mode: Letter
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MATH 382 - Teaching K-8 Mathematics II
Investigations of mathematics topics that focus on proportional thinking, measurement, and informal geometry. Emphasis on problem solving, the use of manipulatives and computing technologies, remediation and resource materials, and optimal pedagogical techniques that help students learn quality mathematics. Not acceptable for any department major except BA/Ed, Elementary, and does not satisfy GUR mathematics requirement except for those who complete the BA/Ed, Elementary.
Prerequisites & Notes:
MATH 381 with a C or better
Credits: 4
Grade Mode: Letter
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MATH 383 - Teaching K-8 Mathematics III
Investigations of mathematics topics that focus on probability and statistics. Emphasis on problem solving, the use of manipulatives and computing technologies, remediation, assessment and resource materials, and optimal pedagogical techniques that help students learn quality mathematics. Not acceptable for any departmental major except BA/Ed, Elementary.
Prerequisites & Notes:
MATH 382 with a C or better at WWU
Credits: 4
Grade Mode: Letter
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MATH 401 - Introduction to Abstract Algebra
Introduction to groups, Lagrange’s Theorem, isomorphisms and homomorphisms, normal subgroups and factor groups, the fundamental theorem of finite abelian groups.
Prerequisites & Notes:
MATH 204; and MATH 302 or MATH 309.
Credits: 4
Grade Mode: Letter
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MATH 402 - Introduction to Abstract Algebra
Introduction to rings and fields, ideals, polynomial rings, unique factorization domains, field extensions, finite fields.
Prerequisites & Notes:
MATH 401
Credits: 4
Grade Mode: Letter
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MATH 409 - Putnam Exam Preparation
Preparation for participation in the annual Putnam Exam. This exam involves mathematical concepts beyond those typically found in standard courses. Questions cut across the bounds of disciplines and are hard. This course covers the basics of the relevant mathematical content, particularly in discrete mathematics, and emphasizes advanced problem-solving techniques. S/U grading.
Prerequisites & Notes:
Permission of instructor.
Credits: 2
Grade Mode: S/U
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MATH 410 - Mathematical Modeling
The construction and solution of mathematical models, using optimization, stability analysis, eigenvalue methods, probability and simulation.
Prerequisites & Notes:
MATH 204, MATH 224, MATH 331
Credits: 4
Grade Mode: Letter
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MATH 412 - Mathematical Modeling Competition
Preparation for participation in the national mathematics modeling competition. Repeatable with no maximum.
Prerequisites & Notes:
instructor permission
Credits: 1
Grade Mode: Letter
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MATH 415 - Mathematical Biology
An introduction to mathematical models in biology. Population models, Michaelis-Menten kinetics, models for neuron functioning, pattern formation. Mathematical topics: difference equations, dynamical systems, conservation equations, stochastic models.
Prerequisites & Notes:
MATH 224; either MATH 204 and MATH 331, or MATH 203 and MATH 303
Credits: 4
Grade Mode: Letter
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MATH 419 - Historical Perspectives of Mathematics
History and development of mathematical thought from ancient to modern times. Philosophical, sociological and biographical perspectives.
Prerequisites & Notes:
12 credits upper-division math
Credits: 3
Grade Mode: Letter
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MATH 420 - Topics in the History and Philosophy of Mathematics
Concentrated study of a topic or a closely connected group of topics associated with the history and philosophy of mathematics. Students are required to write a substantial expository paper.
Prerequisites & Notes:
MATH 312
Credits: 3
Grade Mode: Letter
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MATH 421 - Methods of Mathematical Analysis I
Introduction to metric spaces, properties of functions on metric spaces, compactness and continuity. The student is expected to develop competence in proving basic theorems involving these concepts.
Prerequisites & Notes:
MATH 312
Credits: 4
Grade Mode: Letter
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MATH 422 - Methods of Mathematical Analysis II
Analysis on the real line, including uniform convergence of series, using metric space notions. The student is expected to develop competence in proving theorems involving these concepts.
Prerequisites & Notes:
MATH 421
Credits: 4
Grade Mode: Letter
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MATH 424 - Topics in Analysis
Topics such as pointwise convergence of Fourier series, Gibbs phenomenon, Poisson summability, Dirichlet problem for the disc, Weierstrass approximation theorem. Repeatable to a maximum of 8 credits with various topics.
Prerequisites & Notes:
Math 422
Credits: 4
Grade Mode: Letter
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MATH 430 - Fourier Series and Applications to Partial Differential Equations
An introduction to Fourier series and the Fourier transform; applications to boundary value problems including the wave and heat equations.
Prerequisites & Notes:
MATH 204, MATH 226, MATH 331
Credits: 4
Grade Mode: Letter
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MATH 431 - Analysis of Partial Differential Equations
Solutions for general first order and linear second order partial differential equations. Topics from characteristics; propagation of singularities; hyperbolic, and elliptic equations; Cauchy problem; Dirichlet problem; Green’s function; Poisson formula; maximum principle.
Prerequisites & Notes:
MATH 204, MATH 225, MATH 226, MATH 312, MATH 331, or equivalent(s).
Credits: 4
Grade Mode: Letter
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MATH 432 - Systems of Differential Equations
Forced second order equations, systems of nonlinear differential equations, applications.
Prerequisites & Notes:
MATH 204, MATH 331; or MATH 203, MATH 303.
Credits: 4
Grade Mode: Letter
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MATH 438 - Introduction to Complex Variables
Differentiation and integration of complex-valued functions; Cauchy integral theorem; calculations of residues.
Prerequisites & Notes:
MATH 225 and MATH 312
Credits: 4
Grade Mode: Letter
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MATH 441 - Probability
Discrete and continuous random variables, moment generating functions, multivariate distributions, survey of widely used distributions such as normal, chi-square, gamma, t and F distributions. Emphasis on the theoretical aspects of probability.
Prerequisites & Notes:
MATH 204, MATH 224, MATH 312
Credits: 4
Grade Mode: Letter
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MATH 442 - Mathematical Statistics
Limiting distributions, the Central Limit Theorem, statistical inferences such as confidence intervals, hypothesis testing and chi-square tests, maximum likelihood methods, sufficiency.
Prerequisites & Notes:
MATH 441 or equivalent
Credits: 4
Grade Mode: Letter
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MATH 443 - Linear Statistical Models
Matrix algebra for linear models, multivariate normal distribution, quadratic forms, Gauss-Markov Theorem, estimation in full-rank and less-than-full-rank models, hypothesis testing in full-rank models.
Prerequisites & Notes:
MATH 441/541, and either MATH 342 or MATH 442/542, or equivalent(s).
Credits: 4
Grade Mode: Letter
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MATH 473 - Numerical Linear Algebra
Norms; fundamental matrix types, transformations and factorizations; linear equations, linear least squares; rounding error, condition and stability; the algebraic eigenvalue problem (QR method).
Prerequisites & Notes:
MATH 304; ability to program.
Credits: 4
Grade Mode: Letter
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MATH 483 - Methods of Teaching Secondary Mathematics
Topics include pre-algebra, algebra, geometry, problem solving and resource materials.
Prerequisites & Notes:
Minimum of two upper-division math courses, SEC 431, or permission of instructor.
Credits: 4
Grade Mode: Letter
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MATH 490 - Senior Project
Intensive study of an advanced topic in mathematics.
Prerequisites & Notes:
Permission of the Department Chair.
Credits: 4
Grade Mode: Letter
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MATH 491 - Internship Seminar - Teaching K-8 Mathematics
Focus on issues and practices related to teaching K-8 mathematics, coordinated with the year-long K-8 classroom internship. Includes the use of ideas, theory, and lesson plans from the Mathematics 381-383 sequence in actual classroom settings, plus opportunity to assess and work with K-8 students on an individual, small group, and whole class basis. Not acceptable for any departmental major except BA/Ed, Elementary. S/U grading.
Prerequisites & Notes:
completion of WWU Elementary Education degree requirement
Credits: 2
Grade Mode: S/U
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MATH 495 - Academic or Industrial Learning and Research Experience in Math
Participation in a learning program, research project or internship in business, industry, a government agency or academic institution. Oral and written report required. Repeatable to a maximum of 8 cr. S/U grading.
Prerequisites & Notes:
20 credits math above the 100-level; department permission
Credits: 1-4
Grade Mode: S/U
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MATH 502 - Abstract Algebra
Introduction to rings and fields, ideals, polynomial rings, unique factorization domains, field extensions, finite fields.
Prerequisites & Notes:
MATH 401 or equivalent
Credits: 4
Grade Mode: Letter
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MATH 503 - Topics in Abstract Algebra
Topics such as Galois theory, number theory, group representation theory, algebraic geometry, Lie algebras. Repeatable with various topics.
Prerequisites & Notes:
MATH 502 or equivalent
Credits: 3
Grade Mode: Letter
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MATH 504 - Abstract Linear Algebra
Abstract vector spaces, linear transformations, spectral theory.
Prerequisites & Notes:
MATH 304 or equivalent
Credits: 4
Grade Mode: Letter
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MATH 510 - Mathematical Modeling
The construction and solution of mathematical models, using optimization, stability analysis, eigenvalue methods, probability and simulation.
Prerequisites & Notes:
MATH 204, MATH 224, MAtH 331
Credits: 4
Grade Mode: Letter
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MATH 511 - Advanced Modeling
Exact and numerical techniques for the development and analysis of models of dynamic processes, including the construction and validation of models.
Prerequisites & Notes:
MATH 331; instructor permission
Credits: 4
Grade Mode: Letter
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MATH 515 - Mathematical Biology
An introduction to mathematical models in biology. Population models, Michaelis-Menten kinetics, models for neuron functioning, pattern formation. Mathematical topics: difference equations, dynamical systems, conservation equations, stochastic models.
Prerequisites & Notes:
MATH 224; MATH 204 and MATH 331 or MATH 203 and MATH 303
Credits: 4
Grade Mode: Letter
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MATH 521 - Methods of Mathematical Analysis I
Introduction to metric spaces, properties of functions on metric spaces, compactness and continuity.
Credits: 4
Grade Mode: Letter
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MATH 522 - Methods of Mathematical Analysis II
Analysis on the real line, including uniform convergence of series, using metric space notions.
Prerequisites & Notes:
MATH 521
Credits: 4
Grade Mode: Letter
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MATH 523 - Advanced Calculus of Several Variables
Parameterization, integration and changes of variables in Euclidean spaces.
Prerequisites & Notes:
MATH 304 or equivalent; MATH 521
Credits: 4
Grade Mode: Letter
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MATH 524 - Topics in Analysis
Topics such as pointwise convergence of Fourier series, Gibbs phenomenon, Poisson summability, Dirichlet problem for the disc, Weierstrass approximation theorem. Repeatable to a maximum of 8 credits with various topics.
Prerequisites & Notes:
MATH 522
Credits: 4
Grade Mode: Letter
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MATH 525 - Topology
Topological spaces, connectedness, compactness, product and quotient spaces, homotopy.
Prerequisites & Notes:
MATH 521
Credits: 3
Grade Mode: Letter
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MATH 527 - Real Analysis
Theory of Lebesgue measure and integration.
Prerequisites & Notes:
MATH 522
Credits: 4
Grade Mode: Letter
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MATH 528 - Functional Analysis
Spaces of functions, linear functionals and their representation, applications.
Prerequisites & Notes:
MATH 522
Credits: 4
Grade Mode: Letter
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MATH 530 - Fourier Series and Applications to Partial Differential Equations
An introduction to Fourier series and the Fourier transform; applications to boundary value problems including the wave and heat equations.
Prerequisites & Notes:
MATH 204, MATH 226, MATH 331 or equivalent
Credits: 4
Grade Mode: Letter
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MATH 531 - Analysis of Partial Differential Equations
Solutions for general first order and linear second order partial differential equations emphasizing geometric properties and integral representations. Topics include characteristics; propagation of singularities; hyperbolic, elliptic, and parabolic equations; Cauchy problem; Dirichlet problem; Green’s function; Poisson formula; maximum principle.
Prerequisites & Notes:
MATH 204, MATH 225, MATH 226, MATH 312, MATH 331, or equivalent.
Credits: 4
Grade Mode: Letter
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MATH 533 - Advanced Ordinary Differential Equations
Existence and uniqueness of solutions, stability theory for nonlinear equations, bifurcation.
Prerequisites & Notes:
MATH 432 or equivalent; MATH 521
Credits: 3
Grade Mode: Letter
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MATH 535 - Nonlinear Optimization
Nonlinear programming with emphasis on basic theory (including Lagrange multipliers and the Kuhn-Tucker conditions), algorithms for numerical solution of problems, and applications. Introductory dynamic programming, with emphasis on applications and algorithms.
Prerequisites & Notes:
MATH 204, MATH 224; CSCI 140 or CSCI 141 or MATH 207.
Credits: 4
Grade Mode: Letter
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MATH 538 - Complex Variables
Differentiation and integration of complex-valued functions, Cauchy integral theorem, residues.
Prerequisites & Notes:
MATH 312 or equivalent.
Credits: 4
Grade Mode: Letter
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MATH 539 - Topics in Complex Analysis
Topics such as normal families, mapping properties of analytic functions, conformal mappings, fluid flow, Dirichlet and Neumann problems, Julia sets. Repeatable with various topics.
Prerequisites & Notes:
MATH 521, MATH 538
Credits: 3
Grade Mode: Letter
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MATH 541 - Probability
Discrete and continuous random variables, moment generating functions, multivariate distributions, survey of widely used distributions such as normal, chi-square, gamma, t and F distributions. Emphasis on the theoretical aspects of probability.
Prerequisites & Notes:
MATH 204, MATH 224, MATH 312
Credits: 4
Grade Mode: Letter
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MATH 542 - Mathematical Statistics
Limiting distributions, the Central Limit Theorem, statistical inferences such as confidence intervals, hypothesis testing and chi-square tests, maximum likelihood methods, sufficiency.
Prerequisites & Notes:
MATH 441 or equivalent
Credits: 4
Grade Mode: Letter
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MATH 543 - Linear Statistical Models
Matrix algebra for linear models, multivariate normal distribution, quadratic forms, Gauss-Markov Theorem, estimation in full-rank and less-than-full-rank models, hypothesis testing in full-rank models.
Prerequisites & Notes:
MATH 441/541, and either MATH 342 or MATH 442/542 or equivalent(s).
Credits: 4
Grade Mode: Letter
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MATH 545 - Topics in Probability
Topics from Markov and sequential decision processes, renewal theory, inventory theory, stochastic control, random arrival and service processes, waiting time, number in queue, bulk arrivals, networks, balking. Repeatable with various topics.
Prerequisites & Notes:
MATH 541
Credits: 3
Grade Mode: Letter
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MATH 560 - Topics in Geometry
A study of one or more topics in geometry such as convex sets, polytopes, tilings, integral geometry or combinatorial geometry. Repeatable with various topics.
Credits: 3
Grade Mode: Letter
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MATH 562 - Differential Geometry
Geometry of curves, surfaces and manifolds.
Prerequisites & Notes:
MATH 522
Credits: 4
Grade Mode: Letter
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MATH 564 - Graph Theory
Basic properties of graphs, trees, Eulerian and Hamiltonian circuits, genera of graphs, algorithms, applications.
Credits: 3
Grade Mode: Letter
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MATH 566 - Topics in Combinatorics
Counting techniques, generating functions, coding, coloring and relations with probability theory. Repeatable with various topics.
Credits: 3
Grade Mode: Letter
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MATH 570 - Topics in Optimization
Topics taken from nonlinear programming, calculus of variations or the theory of optimal control. Repeatable with various topics.
Prerequisites & Notes:
MATH 304, MATH 521
Credits: 4
Grade Mode: Letter
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MATH 573 - Numerical Linear Algebra
Norms; fundamental matrix types, transformations and factorizations; linear equations, linear least squares; rounding error, condition and stability; the algebraic eigenvalue problem (QR method).
Prerequisites & Notes:
MATH 304; ability to program
Credits: 4
Grade Mode: Letter
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MATH 575 - Numerical Analysis
Polynomial interpolation including splines, orthogonal systems of functions and least squares approximation; numerical differentiation and integration; solution of systems of nonlinear equations and unconstrained optimization.
Prerequisites & Notes:
MATH 224, M/CS 375
Credits: 4
Grade Mode: Letter
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MATH 577 - Topics in Numerical Analysis
Topics from numerical optimization, approximation, linear algebra, quadrature, and the solution of algebraic and differential equations. Repeatable with various topics.
Prerequisites & Notes:
MATH 573 or M/CS 375
Credits: 4
Grade Mode: Letter
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