Pennsylvania State University-Penn State Erie-Behrend College · Courses
MATH
169 courses with the subject MATH, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MATH 033Mathematics for Sustainability (3) (GQ) This course is3
one of several offered by the mathematics department with the goal of helping students from non-technical majors partially satisfy their general education quantification requirement. It is designed to provide an introduction to various mathematical modeling techniques, with an emphasis on examples related to environmental and economic sustainability. The course may be used to fulfill three credits of the GQ requirement for some majors, but it does not serve as a prerequisite for any mathematics courses and should be treated as a terminal course. The course provides students with the mathematical background and quantitative reasoning skills necessary to engage as informed citizens in discussions of sustainability related to climate change, resources, pollution, recycling, economic change, and similar matters of public interest. Students apply these skills through writing projects that require quantitative evidence to support an argument. The mathematical content of the course spans six key areas: "measuring" (representing information by numbers, problems of measurement, units, estimation skills); "flowing" (building and analyzing stock-flow models, calculations using units of energy and power, dynamic equilibria in stock-flow systems, the energy balance of the earth-sun system and the greenhouse effect); "connecting" (networks, the bystander effect, feedbacks in stock-flow models); "changing" (out-of-equilibrium stock-flow systems, exponential models, stability of equilibria in stock-flow systems, sensitivity of equilibria to changes in a parameter, tipping points in stock-flow models); "risking" (probability, expectation, bayesian inference, risk vs uncertainty; "deciding" (discounting, uses and limitations of cost-benefit analysis, introduction to game theory and the tragedy of the commons, market- based mechanisms for pollution abatement, ethical considerations). RECOMMENDED PREPARATIONS: ENGL 15 Bachelor of Arts: Quantification General Education: Quantification (GQ) GenEd Learning Objective: Effective Communication GenEd Learning Objective: Crit and Analytical Think GenEd Learning Objective: Key Literacies GenEd Learning Objective: Soc Resp and Ethic Reason MATH 34: The Mathematics of Money This course will provide students with the mathematical background and quantitative skills needed to make sound financial decisions. This course introduces personal finance topics including simple interest, simple discount, compound interest, annuities, investments, retirement plans, inflation, depreciation, taxes, credit cards, mortgages, and car leasing. Students will learn how to use linear equations, exponential and logarithmic equations, and arithmetic and geometric sequences to solve real world financial problems. Students will answer questions such as, What is the most they can afford to pay for a car? How much do they need to invest in their 401(k) account each month to retire comfortably? What credit card is the best option? In a society where consumers are presented with a vast array of financial products and providers, students are enabled to evaluate options and make informed, strategic decisions. This course may be used by students from non-technical majors to satisfy 3 credits of their General Education Quantification (GQ) requirement. This course does not serve as a prerequisite for any mathematics courses and should be treated as a terminal course. Enforced Prerequisite at Enrollment: MATH 4 or satisfactory performance on the mathematics placement exam Bachelor of Arts: Quantification General Education: Quantification (GQ) GenEd Learning Objective: Crit and Analytical Think GenEd Learning Objective: Key Literacies MATH 35: General View of Mathematics This course presents a general view of a number of mathematical topics to a non-technical audience, often relating the mathematical topics to a historical context, and providing students with an opportunity to engage with the mathematics at an introductory level. Although some variation in topics covered may take place among different instructors at different campuses, an example of such a course focuses on a number theory theme throughout the course, beginning with the Greeks' view of integers, the concept of divisors, the calculation of greatest common divisors (which originates with Euclid), the significance of the prime numbers, the infinitude of the set of prime numbers (also known to the ancient Greeks), work on perfect numbers (which continues to be a topic of research today), and the work of Pythagoras and his famous Theorem. The course then transitions to the work of European mathematicians such as Euler and Gauss, including work on sums of two squares (which generalizes the Pythagorean Theorem), and then considering Euler's phi function, congruences, and applications to cryptography. Bachelor of Arts: Quantification General Education: Quantification (GQ)
This summer course aims to provide incoming students with the tools needed to be successful wherever they place in the calculus sequence. Specific content is tailored to individual students, based on their existin skill set and expected entry point in the calculus sequence, but ranges from algebra and trigonometry to the real analysis which underlies calculus. The course emphasizes teamwork, communication skills, growth mindset, self-assessment (e.g., metacognition) and building a community of scholars. This is achieved through evidence-based, student-centered pedagogical practices such as collaborative and active learning, scaffolded instruction, extensive group work, metacognitive reflections, and exploratory projects and presentations.
or MATH 141 Calculus with Analytic Geometry II Supporting Courses and Related Areas Select 12 credits of specialization/minor courses in consultation with 12 adviser Select 3 credits in communications/sustainability/leadership 3 oil General Education Connecting career and curiosity, the General Education curriculum provides the opportunity for students to acquire transferable skills 3 necessary to be successful in the future and to thrive while living in interconnected contexts. General Education aids students in developing intellectual curiosity, a strengthened ability to think, and a deeper sense of aesthetic appreciation. These are requirements for all baccalaureate students and are often partially incorporated into the requirements of a program. For additional information, see the General Education with 18 Requirements (p. 3371) section of the Bulletin and consult your academic adviser. The keystone symbol appears next to the title of any course that is Credits designated as a General Education course. Program requirements may also satisfy General Education requirements and vary for each program. 4 Foundations (grade of C or better is required and Inter-Domain 3 courses do not meet this requirement.) • Quantification (GQ): 6 credits 3 • Writing and Speaking (GWS): 9 credits Breadth in the Knowledge Domains (Inter-Domain courses do not meet this requirement.) 3 • Arts (GA): 3 credits 3 • Health and Wellness (GHW): 3 credits • Humanities (GH): 3 credits 4 • Social and Behavioral Sciences (GS): 3 credits 3 • Natural Sciences (GN): 3 credits
Requirements for the Option Credits Select an option 27 3 Requirements for the Option Community and Economic Development Option (27 credits) Code Title Credits
MATH 140ECalculus with Engineering Applications I4
Calculus is an important building block in the education of any professional who uses quantitative analysis. This course introduces and develops the mathematical skills required for analyzing change and creating mathematical models that replicate real-life phenomena. The goals of our calculus courses include to develop the students' knowledge of calculus techniques and to use the calculus environment to develop critical thinking and problem solving skills. The concept of limit is central to calculus; MATH 140E begins with a study of this concept. Differential calculus topics include derivatives and their applications to rates of change, related rates, linearization, optimization, and graphing techniques. The Fundamental Theorem of Calculus, relating differential and integral calculus begins the study of Integral Calculus. Antidifferentiation and the technique of substitution is used in integration applications of finding areas of plane figures and volumes of solids of revolution. Trigonometric functions are included in every topic. Enforced Prerequisite at Enrollment: Math 22 and Math 26 or Math 26 and satisfactory performance on the mathematics placement examination or Math 40 or Math 41 or satisfactory performance on the mathematics placement examination. Bachelor of Arts: Quantification General Education: Quantification (GQ) GenEd Learning Objective: Crit and Analytical Think GenEd Learning Objective: Key Literacies
MATH 140GCalculus with Earth and Mineral Sciences Applications I4
This course is the first in a sequence of three calculus courses designed for students in the earth and mineral sciences and related fields. Topics include limits of functions, continuity; the definition of the derivative, various rules for computing derivatives (such as the product rule, quotient rule, and chain rule), implicit differentiation, higher- order derivatives, solving related rate problems, and applications of differentiation such as curve sketching, optimization problems, and Newton's method; the definition of the definite integral, computation of areas, the Fundamental Theorem of Calculus, integration by substitution, and various applications of integration such as computation of areas between two curves, volumes of solids, and work. Enforced Prerequisite at Enrollment: Math 22 and Math 26 or Math 26 and satisfactory performance on the mathematics placement examination or Math 40 or Math 41 or satisfactory performance on the mathematics placement examination. Bachelor of Arts: Quantification General Education: Quantification (GQ) GenEd Learning Objective: Crit and Analytical Think GenEd Learning Objective: Key Literacies
MATH 140HHonors Calculus with Analytic Geometry I4
Calculus is an important building block in the education of any professional who uses quantitative analysis. This course introduces and develops the mathematical skills required for analyzing change and creating mathematical models that replicate real-life phenomena.
Techniques of integration and applications to biology; elementary matrix theory, limits of matrices, Markov chains, applications to biology and the natural sciences; elementary and separable differential equations, linear rst-order differential equations, linear systems of differential equations, the Lotka-Volterra equations. Students may take only one course for credit from MATH 141, 141B, and 141H. Enforced Prerequisite at Enrollment: MATH 140 or MATH 140A or MATH 140B or MATH 140E or MATH 140G or MATH 140H. Bachelor of Arts: Quantification General Education: Quantification (GQ) GenEd Learning Objective: Crit and Analytical Think GenEd Learning Objective: Key Literacies
MATH 141ECalculus with Engineering Applications II4
MATH 141E is the second course in a two- or three-course calculus sequence for students in science, engineering and related fields. Calculus is an important building block in the education of any professional who uses quantitative analysis. This course further introduces and develops the mathematical skills required for analyzing growth and change and creating mathematical models that replicate reallife phenomena. The goals of our calculus courses include to develop the students' knowledge of calculus techniques and to use the calculus environment to develop critical thinking and problem solving skills. This course covers the following topics: logarithms, exponentials, and inverse trigonometric functions; applications of the definite integral and techniques of integration; sequences and series; power series and Taylor polynomials; parametric equations and polar functions. Enforced Prerequisite at Enrollment: MATH 140 or MATH 140A or MATH 140B or MATH 140E or MATH 140G or MATH 140H. Bachelor of Arts: Quantification General Education: Quantification (GQ) GenEd Learning Objective: Crit and Analytical Think GenEd Learning Objective: Key Literacies
MATH 141GCalculus with Earth and Mineral Sciences Applications II4
This course is the second in a sequence of three calculus courses designed for students in the earth and mineral sciences and related fields. Topics include inverse functions of exponential, logarithmic, and trigonometric functions; indeterminate forms and L'Hopital's rule; various techniques of integration, including integration by parts, trigonometric integrals, trigonometric substitution, and partial fractions; improper integration; infinite sequences and series, tests for convergence and divergence of infinite series, including the integral test, comparison tests, ratio test, root test; power series, Taylor and MacLaurin Series. Enforced Prerequisite at Enrollment: MATH 140 or MATH 140A or MATH 140B or MATH 140E or MATH 140G or MATH 140H. Bachelor of Arts: Quantification General Education: Quantification (GQ) GenEd Learning Objective: Crit and Analytical Think GenEd Learning Objective: Key Literacies
MATH 141HHonors Calculus with Analytic Geometry II4
MATH 141 is the second course in a two- or three-course calculus sequence for students in science, engineering and related fields. Calculus is an important building block in the education of any professional who uses quantitative analysis. This course further introduces and develops the mathematical skills required for analyzing growth and change and creating mathematical models that replicate reallife phenomena. The goals of our calculus courses include to develop the students' knowledge of calculus techniques and to use the calculus environment to develop
/Maximum of 9 Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest. Bachelor of Arts: Quantification
/Maximum of 9 Formal courses given on a topical or special interest subject offered infrequently; several different topics may be taught in one year or semester. This Special Topics is a GenEd course.
Fundamental concepts of arithmetic and geometry, including problem solving, number systems, and elementary number theory. For elementary and special education teacher certification candidates only. A student who has passed EDMTH 444 may not take MATH 200 for credit.
This course studies the foundations of elementary school mathematics with an emphasis on problem solving. MATH 201 Problem Solving in Mathematics II (3) (GQ) Problem Solving in Mathematics II studies the foundations of elementary school mathematics with an emphasis on problem solving. Mathematical ways of thinking are integrated throughout the study of probability, statistics, graphing, geometric shapes, and measurement. This course is designed for prospective teachers not only to gain the ability to explain the mathematics in elementary school courses, but also to help them comprehend the underlying mathematical concepts. Gaining a deeper understanding will enable them to assist their young students in the classroom since effective mathematical teaching requires understanding what students know, what they need to learn, and then helping them to learn it well. General Education: Quantification (GQ) GenEd Learning Objective: Crit and Analytical Think GenEd Learning Objective: Key Literacies
3 Applications 3 or MATH 141 Calculus with Analytic Geometry II 2 MATH 250 Ordinary Differential Equations 1 or MATH 211 Intermediate Calculus and Differential Equations with 3 Applications 2 Select 3 credits from the following: 3 3 CAS 100 Effective Speech 3 CAS 100A Effective Speech 3 CAS 100B Effective Speech 4 Select 3-5 credits from the following: 3-5 3 MATH 26 Plane Trigonometry and Applications of
Honors course in three-dimensional analytic geometry; vectors in space; partial differentiation; double and triple integrals; integral vector calculus. Students who have passed either MATH 231 or MATH 232 may not schedule MATH 230 or MATH 230H for credit. MATH 230H Honors Calculus and Vector Analysis (4) This course is the third in a sequence of three calculus courses designed for students in engineering, science, and related fields. Topics include vectors in space, dot products, cross products; vector-valued functions, modeling motion, arc length, curvature; functions of several variables, limits, continuity, partial derivatives, directional derivatives, gradient vectors, Lagrange multipliers;
& MATH 232 and Integral Vector Calculus Requirements for the Option Select an option 27 The following substitutions are allowed for students attending campuses where the indicated courses is not offered: CAS 100A, ENGL 138T or ENGL 202C can be substituted for EMSC 100S. Students who complete Basic ROTC may substitute 6 credits of ROT for 3 credits of GHW courses and 3 credits of electives. Requirements for the Option Atmospheric Science Option (27-28 credits) Code Title Cre
Multidimensional analytic geometry, double and triple integrals; potential fields; flux; Green's, divergence and Stokes' theorems. Students who have passed MATH 230 may not schedule this course for credit. Enforced Prerequisite at Enrollment: MATH 231 or MATH 231H Bachelor of Arts: Quantification
MATH 240Mathematical Methods for Biology and the Life Sciences4
This course will cover systems of differential equations, multivariable calculus, and applications to biology and the life sciences. Students will learn about complex numbers, and their relation to oscillations. Analysis of biologically relevant mathematical models will include the linear stability of couples nonlinear systems, and the method of separation of timescales. The course will also introduce probability theory in a biological context, including conditional probability, Bayes Theorem, probability distributions, and stochastic modeling in the life sciences. Enforced Prerequisites at Enrollment: MATH141B or instructor approval
MATH 251Ordinary and Partial Differential Equations4
or MATH 250 Ordinary Differential Equations & MATH 252 and Partial Differential Equations Supporting Courses and Related Areas Select 3 credits of 400-level MATH from departmental list 3 Requirements for the Option Select an option 24-27
MATH 251HHonors Ordinary and Partial Differential Equations4
This course serves as an introduction to ordinary and partial differential equations. Topics include various techniques for solving first and second order ordinary differential equations, an introduction to numerical methods, solving systems of two ordinary differential equations, nonlinear differential equations and stability, Laplace transforms, Fourier series, and partial differential equations. In contrast to the non-honors version of this course, the honors version is typically more theoretical and will often include more sophisticated problems. Moreover, certain topics are often discussed in more depth and are sometimes expanded to include applications which are not visited in the non-honors version of the course. Enforced Prerequisite at Enrollment: (MATH 141 or MATH 141B or MATH 141E or MATH 141G or MATH 141H) and (MATH 220 or MATH 220H) Bachelor of Arts: Quantification
Fourier series; partial differential equations. Students who have passed MATH 251 may not schedule this course for credit. This course serves as the continuation of MATH 250 (Ordinary Differential Equations) and provides an elementary treatment of partial differential equations and Fourier series. Once a student completes both MATH 250 (3 credits) and MATH 252 (1 credit), the student will have completed all of the material in MATH 251 (4 credits). In particular, the student will be able to find solutions to given partial differential equations and will be able to utilize the tools from the field of Fourier series in the process.
/Maximum of 18 Creative projects, including nonthesis research, which are supervised on an individual basis and which fall outside the scope of formal courses. Bachelor of Arts: Quantification
/Maximum of 9 Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest. Bachelor of Arts: Quantification
Basic methods of mathematical thinking and fundamental mathematical structures, primarily in the context of numbers, groups, and symmetries Bachelor of Arts: Quantification
Select 3 credits from the following: STAT/MATH Elementary Probability 318 STAT/MATH Introduction to Probability Theory 414 STAT/MATH Introduction to Probability and Stochastic 418 Processes for Engineering Supporting Courses and Related Areas Select 12 credits from the lists of Application Focus courses; 6 credits must at at the 300- or 400-levels. Students may apply up to 3 credits of ROTC as option Applicatio Focus list credits and 3 credits of ROTC as GHW credits. LIST OF APPLIED DATA SCIENCES COURSES (p. 1118) Computational Data Sciences (DTSCE_BS): 47 credits Only Available through the College of Engineering
Supporting Courses and Related Areas Supporting Courses and Related Areas: Require a grade of C or better Select 12 credits of 400-level MATH courses 12 No more than 3 credits of MATH 400 may be used for this requirement.
This course provides rigorous development of the key concepts and results of analysis. The topics include sequences and continuity of functions in the context of real numbers and metric spaces, series, differentiation and integration of functions on the real line. Enforced Prerequisite at Enrollment: (MATH 141 or MATH 141B or MATH 141E or MATH 141G or MATH 141H) and (MATH 311M or (MATH 311W and permission of the instructor)) Bachelor of Arts: Quantification
Development thorough understanding and technical mastery of foundations of modern geometry. MATH 313H Concepts of Geometry (3) The central aim of this course is to develop thorough understanding and technical mastery of foundations of modern geometry. Basic high school geometry is assumed; axioms are mentioned, but not used to deduce theorems. Approach in development of the Euclidean geometry of the plane and the 3-dimensional space is mostly synthetic with an emphasis on groups of transformations. Linear algebra is invoked to clarify and generalize the results in dimension 2 and 3 to any dimension. It culminates in the last part of the course where six 2-dimensional geometries and their symmetry groups are discussed. This course is a a part of a new "pre-MASS" program (PMASS)aimed at freshman/ sophomore level students, which will operate in steady state in the spring semesters. This course is directly linked with a proposed course Math . 313R, its 1-credit recitation component. It is highly recommended to all mathematics, physics and natural sciences majors who are graduate school bound, and is a great opportunity for all Schreyer Scholars. The following topics will be covered: Euclidean geometry of the plane (distance, isometries, scalar product of vectors, examples of isometries: rotations, reflections, translations, orientation, symmetries of planar figures, review of basic notions of group theory, cyclic and dihedral groups, classification of isometries of Euclidean plane, discrete groups of isometries and crystallographic restrictions. similarity transformations, selected results from classical Euclidean geometry}; Euclidean geometry of the 3-dimensional space and the sphere (distance, isometries, scalar product of vectors, planes and lines in the 3-dimensional space, normal vectors to planes, classification of pairs of lines, isometries with a fixed point: rotations and reflections, orientation, isometries of the sphere, classification of orientation-reversing isometries with a fixed point, finite groups of isometries of the 3-dimensional space, existence of a fixed point, examples: cyclic, dihedral, and groups of symmetries of Platonic solids, classification of isometries without fixed point: translations and screw-motions, intrinsic geometry of the sphere, elliptic plane: a first example of non-Euclidean geometry); Elements of linear algebra and its application to geometry in 2, 3, and n dimension (real and complex vector l spaces. linear independence of vectors, basis and dimension, eigenvalues s and eigenvectors, diagonalizable matrices, classification of matrices in dimension 2: elliptic, hyperbolic and parabolic matrices, orthogonal matrices and isometries of the n-dimensional space); Six 2-dimensional geometries (Projective geometry, affine geometry, inversions and conformal geometry, Euclidean geometry revisited, geometry of elliptic plane, hyperbolic geometry). The achievement of educational objectives will be assessed through weekly homework, class participation, and midterm and final exams. Enforced Prerequisite at Enrollment: MATH 140H and MATH 311M or Concurrent: MATH 312H
Combinatorial analysis, axioms of probability, conditional probability an independence, discrete and continuous random variables, expectation, limit theorems, additional topics. Students who have passed either MATH(STAT) 414 or 418 may not schedule this course for credit. Enforced Prerequisite at Enrollment: MATH 141 Cross-listed with: STAT 318 Bachelor of Arts: Quantification
Statistical inference: principles and methods, estimation and testing hypotheses, regression and correlation analysis, analysis of variance, computer analysis. Students who have passed STAT (MATH) 415 may not schedule this course for credit. Enforced Prerequisite at Enrollment: MATH 318 or STAT 318 or MATH 414 or STAT 414 or STAT 418 or MATH 418 Cross-listed with: STAT 319 Bachelor of Arts: Quantification
/Maximum of 9 Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest. Bachelor of Arts: Quantification
BA Fields 3 General Education Course 3 Supporting Course (Chosen 3 General Education Course 3 in consultation wtih an academic adviser) General Education Course 3 Total Credits 119-121 * Course requires a grade of C or better for the major ‡ Course requires a grade of C or better for General Education # Course is an Entrance to Major requirement † Course satisfies General Education and degree requirement To take MATH 412 or MATH 417 in a Spring semester, swap it with MATH 435 or MATH 436 in Third Year Spring or with a MATH 400-level in Fourth Year Spring. To take MATH 421, swap it with MATH 403 in Fourth Year Fall. Excluding MATH 401, MATH 405, MATH 406, MATH 410, MATH 418, MATH 441, MATH 470, MATH 471. At most 2 credits of MATH 400 or 4 MATH 497 Learning Assistant Experience may be used. 4 Bachelor of Arts Requirements:
3 MATH 410 Complex Analysis for Mathematics and 1 Engineering 3 MATH 411 Ordinary Differential Equations 4 MATH 412 Fourier Series and Partial Differential Equations 4 MATH 425 Introduction to Operations Research
This course covers the foundations of classical analysis in the framework of metric spaces. Topics include metric spaces, compactness, continuous maps, uniform convergence, and function spaces. Enforced Prerequisite at Enrollment: (MATH 311M or MATH 311W) and (MATH 312H or (MATH 312 and permission of the instructor)) Bachelor of Arts: Quantification
Differentiation of functions from Rn to Rm, implicit function theorem, Riemann integration, Fubini's theorem, Fourier analysis. Enforced Prerequisite at Enrollment: MATH 403 Bachelor of Arts: Quantification
MATH 405Advanced Calculus for Engineers and Scientists I3
Vector calculus, linear algebra, ordinary and partial differential equations. Students who have passed MATH 411 or 412 may not take this course for credit. Enforced Prerequisite at Enrollment: (MATH 230 or MATH 231) and (MATH 250 or MATH 251) Bachelor of Arts: Quantification
MATH 406Advanced Calculus for Engineers and Scientists II3
Complex analytic functions, sequences and series, residues, Fourier and Laplace transforms. Students who have passed MATH 421 may not take this course for credit. Enforced Prerequisite at Enrollment: MATH 405 Bachelor of Arts: Quantification
MATH 410Complex Analysis for Mathematics and Engineering3
Complex analytic functions; Cauchy-Riemann equations; complex contour integrals; Cauchy's integral formula; Taylor and Laurent series; residue theory; applications in engineering. MATH 410 Complex Analysis for Mathematics and Engineering (3) A succinct stand-alone course description (up to 400 words) to be made available to students through the on-line Bulletin and Schedule of Courses. This is a complex analysis course designed for students in mathematics, applied mathematics, engineering, science, and related fields. Topics include complex numbers; analytic functions, complex differentiability, and the Cauchy-Riemann equations; complex exponential, logarithmic, power, and trigonometric functions; complex contour integrals; Cauchy's theorem; Cauchy's integral formula; Taylor and Laurent series; residue theory; and various applications in areas of science and engineering. This course focuses on the definitions, concepts, calculation techniques, supporting theory, and examples of applications suited to the usage of complex analysis in mathematics, applied mathematics, science, and engineering. Students who have passed MATH 406 or MATH 421 may not take this course for credit. Enforced Prerequisite at Enrollment: MATH 230 or MATH 232
in consultation with an academic adviser) General Education Course 3 Supporting Course (Chosen in consultation with an academic adviser) Supporting Course (Chosen 3 in consultation with an academic adviser) 15 12-13 Total Credits 119-121 * Course requires a grade of C or better for the major ‡ Course requires a grade of C or better for General Education # Course is an Entrance to Major requirement † Course satisfies General Education and degree requirement Credits 1 Computational option students should not take CMPSC 101, 4 CMPSC 200 or CMPSC 201 since CMPSC 122 and CMPSC 132 require 3 CMPSC 121 or CMPSC 131. 3 Select from MATH 310, MATH 452, MATH 457, MATH 468, MATH 484, 3 MATH 485, CMPSC 442. MATH 411 is offered during the Fall and Summer and MATH 412 and MATH 417 are both only offered during the Spring semesters. In order 16 to take MATH 412 or MATH 417 in the Spring semester, swap it with a Computational Course in Third Year Spring or with CMPSC 465 in Credits Fourth Year Spring. 3 University Requirements and General Education Notes: US and IL are abbreviations used to designate courses that satisfy 3 Cultural Diversity Requirements (United States and International Cultures). 3 W, M, X, and Y are the suffixes at the end of a course number used to designate courses that satisfy University Writing Across the Curriculum 15-16 requirement. Credits General Education includes Foundations (GWS and GQ), Knowledge Domains (GHW, GN, GA, GH, GS) and Integrative Studies (Inter-domain) requirements. N or Q (Honors) is the suffix at the end of a course number used to help identify an Inter-domain course, but the inter-domain attribute is used to fill audit requirements. Foundations courses (GWS 3 and GQ) require a grade of 'C' or better. 3 All incoming Schreyer Honors College first-year students at University Park will take ENGL 137H/CAS 137H in the fall semester and ENGL 138T/CAS 138T in the spring semester. These courses carry the GWS designation and satisfy a portion of that General Education requirement. If the student’s program prescribes GWS these courses will 16.5 replace both ENGL 15/ENGL 30H and CAS 100A/CAS 100B/CAS 100C. Each course is 3 credits.
MATH 412Fourier Series and Partial Differential Equations3
Orthogonal systems and Fourier series; derivation and classification of partial differential equations; eigenvalue function method and its applications; additional topics. MATH 412 Fourier Series and Partial Differential Equations (3) (BA) This course meets the Bachelor of Arts degree requirements.The purpose of MATH 412 is to introduce students to the origins, theory, and applications of partial differential equations. Several basic physical phenomena are considered - including flows, vibrations, and diffusions - and used to derive the relevant equations. The fundamentals of the mathematical theory of partial differential equations are motivated and developed for the students through the systematic exploration of these classic physical systems and their corresponding equations: the Laplace, wave, and heat equations. In addition to treating the physical origins of the equations, this course focuses on solving evolution equations as initial value problems on unbounded domains (the Cauchy problem), and also on solving partial differential equations on bounded domains (boundary value problems). There is not one but many techniques for solving these equations, and the course presents some aspect of the expansion in orthogonal functions (including Fourier series), eigenvalue theory, functional analysis, and the use of separation of variables, Fourier transforms, and Laplace transforms to solve PDEs by converting them to ordinary differential equations. This course currently serves a cross-section of students at the university with interests or the need for this advanced subject mathematics, including students majoring in the engineering program, meteorology, physics, and mathematics. This typically includes the most advanced physics, engineering, and meteorology students, as well as mathematics majors with interests in applied mathematics. Enforced Prerequisite at Enrollment: MATH 230 and (MATH 250 or MATH 251) Bachelor of Arts: Quantification
STAT(MATH) 414 is an introduction to the theory of probability for students in statistics, mathematics, engineering, computer science, and related fields. The course presents students with calculus-based probability concepts and those concepts can be used to describe the uncertainties present in real applications. Topics include probability spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems. Students may take only one course from STAT(MATH) 414 and 418. Enforced Prerequisite at Enrollment: MATH 230 or Concurrent: MATH 232 or (MATH 231 and RM 214) Cross-listed with: STAT 414
MATH 414HHonors Introduction to Probability Theory3
This course covers probability spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems. In contrast to the non-honors version of 414, 414H has a stronger focus on a multivariate presentation of core concepts, asymptotic results, and proofs of essential theorems. This emphasis is complemented through more advanced in-class examples, homework problems, and exam questions. Students will also pursue a topic of choice in further depth through a course project. Students may take only one course from STAT(MATH) 414, 414H, and 418. Enforced Prerequisite at Enrollment: MATH 230 or MATH 230H or MATH 232 Cross-listed with: STAT 414H
A theoretical treatment of statistical inference, including sufficiency, estimation, testing, regression, analysis of variance, and chi-square tests. Enforced Prerequisite at Enrollment: MATH 414 or STAT 414 Cross-listed with: STAT 415
Review of distribution models, probability generating functions, transforms, convolutions, Markov chains, equilibrium distributions, Poisson process, birth and death processes, estimation. Enforced Prerequisite at Enrollment: (STAT 318 or MATH 318 or STAT 414 or MATH 414) and (MATH 230 or MATH 232) Cross-listed with: STAT 416
MATH 417Qualitative Theory of Differential Equations3
Linear differential equations, stability of stationary solutions, ordinary bifurcation, exchange of stability, Hopf bifurcation, stability of periodic solutions, applications. MATH 417 Qualitative Theory of Differential Equations (3) (BA) This course meets the Bachelor of Arts degree requirements.The main objective of the course is the qualitative theory of ordinary differential equations such as existence and uniqueness of solutions, dependence on initial data and parameters, and basic stability of solutions for both linear and nonlinear equations. It is designed to introduce students to modern concepts including the bifurcation theory, intermittent (transitional) and chaotic behavior of solutions and dynamical system approach to differential equations. Along the way, a number of applications are discussed and students get familiar with some basic examples illustrating main principles of the theory, such as Lorenz attractor, predator-prey models, etc. The course is completed by students majoring in engineering programs, the sciences, and mathematics. Enforced Prerequisite at Enrollment: MATH 220 and (MATH 250 or MATH 251) Bachelor of Arts: Quantification
Principles of Newtonian, Lagrangian, and Hamiltonian mechanics of particles with applications to vibrations, rotations, orbital motion, and collisions. PHYS 419 / MATH 419 Theoretical Mechanics (3) A second course in classical mechanics, required of all physics majors who typically take it in their 5th or 6th semester. The course includes a review of relevant mathematics, detailed discussions of advanced topics in Newtonian mechanics, introductions to Lagrangian and Hamiltonian dynamics, and applications to such forced oscillations, orbital motion, vibrational motion and normal modes, rigid body motion, and collisions.It is a prerequisite for Physics 461, which is a second semester extension. It is also a valuable background for most 400-level physics courses, especially Physics 410. Enforced Prerequisite at Enrollment: (MATH 230 or MATH 231) and (MATH 250 or MATH 251) and PHYS 212 and PHYS 213 and PHYS 214 Cross-listed with: PHYS 419
Select 6 credits of 400-level MATH courses except MATH 401, MATH 405, MATH 406, MATH 410, MATH 418, MATH 441, MATH 470, MATH 471. No more than 2 credits of MATH 400 may be used. Select an approved sequence of 12 credits in MATH or a related area or an area of application Undergraduate - The Pennsylvania State University 2026-2027 629 Supporting Courses and Related Areas Credits Select 17-18 credits from department list 17-18 Graduate Study Option (50-51 credits) Code Title Credits
Nature of operations research, problem formulation, model construction, deriving solution from models, allocation problems, general linear allocation problem, inventory problems. Enforced Prerequisite at Enrollment: MATH 141 and MATH 220 Bachelor of Arts: Quantification
Plane and space curves; space surfaces; curvature; intrinsic geometry of surfaces; Gauss-Bonnet theorem; covariant differentiation; tensor analysis. Enforced Prerequisite at Enrollment: MATH 401 or MATH 403 Bachelor of Arts: Quantification
Euclidean and various non-Euclidean geometries and their development from postulate systems. Students who have passed MATH 427 may not schedule MATH 471. Enforced Prerequisite at Enrollment: MATH 230 or MATH 231 Bachelor of Arts: Quantification
Research in mathematics education using ideas from Euclidean and non-Euclidean geometry. Students who have passed MATH 471 may not schedule MATH 427. MATH 428 Geometry for Teachers (1) MATH 428 is designed to introduce students to mathematics education and research in education. The student will present topics in written and verbal classroom reports. Students will be evaluated on research papers and classroom presentations of those papers, classroom technology demonstration of geometry topics, and classroom demonstration of teaching geometry.This course supplements MATH 427 by providing the education component that is required by the state of Pennsylvania for obtaining certification in teaching mathematics. This course is offered only at Penn State Erie, The Behrend College. Enforced Prerequisite at Enrollment: MATH 311W . Prerequisite or concurrent: MATH 427 Bachelor of Arts: Quantification
Determinants, matrices, linear equations, characteristic roots, quadratic forms, vector spaces. Students who have passed Math 436 may not schedule this course. Enforced Prerequisite at Enrollment: MATH 220 Bachelor of Arts: Quantification
The course provides a foundational knowledge of the mathematics and mathematical models of finance, primarily of option pricing, hedging, and portfolio optimization. The topics include the definition of various financial securities and instruments (e.g. bonds, stocks, forward contracts, and options), the theory of interest, the No-Arbitrage Principle, measures of return and volatility, the Markowitz model of portfolio theory, the Capital Asset Pricing Model, the pricing of forward contracts, option
Constructing mathematical models of physical phenomena; topics include pendulum motion, polymer fluids, chemical reactions, waves, flight, and chaos. MATH 450 Mathematical Modeling (3) The purpose of the course is to introduce mathematical modeling, i.e., the construction of mathematical structures which capture relevant physical phenomena. The course will systematically explore mathematical ideas and tools used to study the natural world. Particular emphasis will be placed on the process of creating a mathematical model starting from a physical scenario. Typically this process will begin with an experiment either demonstrated in the W. G. Pritchard Lab or performed by the students in class.Once a particular model has been developed, students will use mathematical analysis and experimentation to determine the properties and relevance of the model, and to make predictions. Often the model can be satisfactory; however, many times one also finds new features of the system that are not adequately accounted for in the model, and the process begins again. It is this cycle the course will focus on. For a given phenomenon (e.g., flow of viscous fluid, pendulum motion) several models may be compared and contrasted, and possible simplifications will be discussed.A significant aspect of the course is its laboratory component, in which the students will perform experiments or observe demonstrations. However, the main emphasis will be placed on creating and rigorously analyzing the mathematical aspects of the models. Instead of presenting a finely tuned model for a given phenomenon, this course will try to convey some of the heuristic, intuitive, and mathematical ideas employed in modeling.Examples Undergraduate - The Pennsylvania State University 2026-2027 4533 of physical systems to be considered include: simple and compound pendulum motion, chemical oscillations, water waves, and elastic behavior of polymer solutions.The course is open to a wide range of undergraduate as well as graduate students with majors in mathematics, biology, chemistry, engineering, and physics. The course should be accessible to students with some basic knowledge of mathematical analysis and differential equations. Main topics include: modeling with ordinary differential equations; bifurcation theory and stability; traveling waves in epidemics, chemical reactions, free fluid surfaces, and polymer solutions; fluctuations in nature, stochastic differential equations and chaos. Enforced Prerequisite at Enrollment: (MATH 315 and MATH 430) or MATH 405 or MATH 412 Bachelor of Arts: Quantification
This is an undergraduate course on the introduction of basic mathematical, numerical and practical aspects of deep learning techniques. It will provide students with the mathematical background and also practical tools needed to understand, to analyze and to further develop numerical methods for deep learning and applications. The course is simultaneously geared towards math students who want to learn about the emerging technology of deep learning and also towards students from other fields who are interested in deep learning application but would like to strengthen their theoretical foundation and mathematical understanding. This course will allow students to fulfill 400-level math course requirement for Math Majors/Minors (or for other Majors as approved by student advisor). The course will cover some basic deep learning models such as the basic deep neural networks, convolutional neural networks, training algorithms such as stochastic gradient descent methods, popular data bases such as MNIST and CIFAR and specific applications such as image classifications. Traditional numerical methods such as finite element and multigrid method will also be introduced to motivate and to understand how and why deep neural networks work. Enforced Prerequisite at Enrollment: MATH 220 and (MATH 230 or MATH 231) and (CMPSC 101 or CMPSC 121 or CMPSC 131 or CMPSC 200 or CMPSC 201)
Floating point computation, numerical rootfinding, interpolation, numerical quadrature, direct methods for linear systems. Students may take only one course for credit from MATH 451 and MATH 455. Enforced Prerequisite at Enrollment: (CMPSC 201 or CMPSC 202 or CMPSC 121 or CMPSC 131) and MATH 220 and (MATH 230 or MATH 231) Cross-listed with: CMPSC 455 Bachelor of Arts: Quantification
FLOATING POINT COMPUTATION, NUMERICAL ROOTFINDING, INTERPOLATION, NUMERICAL QUADRATURE, DIRECT METHODS FOR LINEAR SYSTEMS. STUDENTS MAY TAKE ONLY ONE COURSE FOR CREDIT FROM MATH 451 AND MATH 455.
Polynomial and piecewise polynomial approximation, matrix least squares problems, numerical solution of eigenvalue problems, numerical solution of ordinary differential equations. Enforced Prerequisite at Enrollment: MATH 455 Cross-listed with: CMPSC 456 Bachelor of Arts: Quantification
Propositional logic, first-order predicate logic, axioms and rules of inference, structures, models, definability, completeness, compactness. Logic forms the foundation of all mathematical reasoning. To prove a mathematical theorems, one deduces them step by step from basic principles, called axioms, or from other statements previously deduced. Each step of a proof has to be a logically valid rule, such as, for example the modus ponens: "If A holds, and A implies B, then B holds." In Math 457, students will learn how concepts such as axiom, theorem, proof, and truth can be formulated as a mathematical theory, that is, logical reasoning will be studied as a mathematical subject. The simplest kind of logical system is propositional logic. Here, the basic components are whole statements which are either true or false, and which can be combined using logical connectives such AND, OR, or NOT to form new statements. Its simple nature makes propositional logic a good system to introduce many of the basic ideas: syntax and semantics, proof systems, completeness and compactness. However, propositional logic does not capture mathematical reasoning adequately. Therefore, one considers (first-order) predicate logic. Students will learn how formulas are formed according to syntactical rules. They will also study how a mathematical theory is defined as a set of formulas, how a proof is formally defined, and what constitutes a proof system. The syntactical notions above are contrasted with mathematical semantics, which considers structures over which formulas can be interpreted. This way, one can rigorously define whether a formal statement is true in a given mathematical structure, in which case we say the structure is a model of the statement. For example, the integers with addition are a model of the statement "for every x there exists a y such that x+y =0". A central goal of mathematical logic is to explore how the syntactical side (formulas, axioms, proof systems) and the semantical side (mathematical structures such as the additive group of integers) interact. Two fundamental results in this regard will be covered: the completeness theorem says that one can prove a statement from a set of axioms if and only if the statement is true in any structure satisfying all axioms. The compactness theorem, in turn, is an important consequence of the completeness theorem. It has profound implications for the existence and construction of mathematical structures. Students who would like to enroll in Math 457 are required to have some knowledge of mathematical proofs as provided in Math 311W. Bachelor of Arts: Quantification
3 Supporting Courses and Related Areas 3 Supporting Courses and Related Areas: Require a grade of C or better 4 Select 9 credits from a school-approved list 9 Business Option (43 credits) 2 A maximum of 30 credits through the School of Business may be used to 4 fulfill General Education, Major Requirements and Option Requirements. Code Title Credits
, Prime sieves, factoring, computer numeration systems, congruences, multiplicative functions, primitive roots, cryptography, quadratic residues. Students who have passed MATH 465 may not schedule this course. Enforced Prerequisite at Enrollment: CMPSC 360 or MATH 311W Cross-listed with: CMPSC 467 Bachelor of Arts: Quantification
An introduction to algebraic structures and to the axiomatic approach, including the elements of linear algebra. Designed for teachers and prospective teachers. Students who have passed Math 435 may not schedule this course. Enforced Prerequisite at Enrollment: MATH 311W Bachelor of Arts: Quantification
Problem solving oriented introduction to Euclidean and non-Euclidean geometries; construction problems and geometrical transformations via "Geometer's Sketchpad" software. Intended primarily for those seeking teacher certification in secondary mathematics. Students who have passed MATH 427 may not schedule this course. Enforced Prerequisite at Enrollment: MATH 311W Bachelor of Arts: Quantification
Mathematical description, physical concepts, and experimental tests of special and general relativity. MATH 479 / PHYS 479 Special and General Relativity (3) This course is intended as an elective course (within the undergraduate Physics program) for Physics majors to be taken in their senior year. Intended to be cross-listed with MATH, it can also be used in support of a Mathematics minor and, in some options, within the Math program as a program elective as well. The Undergraduate - The Pennsylvania State University 2026-2027 4535 course significantly expands upon the introduction to Special Relativity (SR) seen in PHYS 237, including discussions of experimental tests of SR and applications to relativistic mechanics. It then introduces students to the mathematical machinery required to understand General Relativity (GR), starting with the description of curved spacetimes and geodesics. It discusses solutions to the Einstein equations and surveys the classic tests which established the validity of General Relativity. It concludes with applications of GR in such areas as black hold physics, the generation and detection of gravitational waves, other topics (such as cosmology, relativistic astrophysics, etc.). Enforced Prerequisite at Enrollment: PHYS 237 and PHYS 400 and PHYS 419 and (MATH 250 or MATH 251) and (MATH 230 or MATH 231) Cross-listed with: PHYS 479 Bachelor of Arts: Quantification
MATH 482Mathematical Methods of Operations Research3
Survey of linear and nonlinear programming; mathematics of optimization; queues; simulation. Enforced Prerequisite at Enrollment: MATH 220 and MATH 230 and STAT 301 Bachelor of Arts: Quantification
Introduction to theory and applications of linear programming; the simplex algorithm and newer methods of solution; duality theory. Enforced Prerequisite at Enrollment: MATH 220 and (MATH 230 or MATH 231) Bachelor of Arts: Quantification
Introduction to the theory and applications of graphs and directed graphs. Emphasis on the fundamental theorems and their proofs. Enforced Prerequisite at Enrollment: MATH 311W Bachelor of Arts: Quantification th
/Maximum of 6 The course comprises colloquium style weekly lectures by visitors and by Penn State faculty covering select topics in classical and contemporary mathematics. Some talks will describe math-intense jobs outside of academia and help the students to plan for their future career. The topics of the lectures will be quite advanced, distinguishing it as an honors course. In addition to attending the talks, toward the end of semester, the students will either give a presentation or write an essay on a mathematical topic of their choice or a topic covered in one of the colloquium talks. Enforced Prerequisite at Enrollment: MATH 220 and MATH 230 and (MATH 250 or MATH 251) and (MATH 311W or MATH 311M)
/Maximum of 6 The honors thesis proposal must be approved by the thesis supervisor and the honors adviser and submitted to the Schreyer Honors College prior to scheduling this course. Honors students in Mathematics should register for Math 494H in one or both of their last two semesters. All Schreyer Scholars are required to complete an undergraduate honors thesis. This work represents the culmination of a student's honors experience. Through the thesis, the student demonstrates a command of relevant scholastic work and a personal contribution to that scholarship. The thesis document should capture the relevant background, methods and techniques, as well as describe the details of the completion of the individual project. Bachelor of Arts: Quantification
/Maximum of 18 Supervised off-campus, nongroup instruction including field experiences, practica, or internships. Written and oral critique of activity required. Bachelor of Arts: Quantification
prior approval of proposed assignment by instructor
MATH 496Independent Studies1-18
/Maximum of 18 Creative projects, including research and design, which are supervised on an individual basis and which fall outside the scope of formal courses. Bachelor of Arts: Quantification
/Maximum of 18 Creative projects, including research and design, which are supervised on an individual basis and which fall outside the scope of formal courses.
/Maximum of 999 Formal courses given infrequently to explore, in depth, a comparatively narow subject which may be topical or of special interest. Bachelor of Arts: Quantification
Complex numbers. Holomorphic functions. Cauchy's theorem. Meromorphic functions. Laurent expansions, residue calculus. Conformal maps, topology of the plane. MATH 502 Complex Analysis (3) This course is devoted to the analysis of differentiable functions of a complex variable. This is a central topic in pure mathematics, as well as a vital computational tool. The course covers the following topics: complex numbers, holomorphic functions, Cauchy's theorem, meromorphic functions, Laurent expansions, residue calculus, conformal maps, topology of the plane.
Banach spaces and Hilbert spaces. Dual spaces. Linear operators. Distributors, weak derivatives. Sovolev spaces. Applications to linear differential equations. MATH 503 Functional Analysis (3) This course develops the theory needed to treat linear integral and differential equations, within the framework of infinite-dimensional linear algebra. Applications to some classical equations are presented. The course covers the following topics: Banach and Hilbert spaces, dual spaces, linear operators, distributions, weak derivatives, Sobolev spaces, applications to linear differential equations.
Fundamental concepts; extensive survey of examples; equivalence and classification of dynamical systems, principal classes of asymptotic invariants, circle maps.
First order equations, the Cauchy problem, Cauchy-Kowalevski theorem, Laplace equation, wave equation, heat equation. Graduate - The Pennsylvania State University 2026-2027 1269
MATH 515Classical Mechanics and Variational Methods3
Introduction to the calculus of variations, variational formulation of Lagrangian mechanics, symmetry in mechanical systems, Legendre transformation, Hamiltonian mechanics, completely integrable systems.
Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics. Cross-listed with: STAT 517
Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics. Cross-listed with: STAT 518
Selected topics in stochastic processes, including Markov and Wiener processes; stochastic integrals, optimization, and control; optimal filtering. Cross-listed with: STAT 519
Approximation and interpolation, numerical quadrature, direct methods of numerical linear algebra, numerical solutions of nonlinear systems and optimization. MATH 523 Numerical Analysis I (3) 1. Approximation
Matrix decompositions. Direct method of numerical linear algebra. Eigenvalue computations. Iterative methods. MATH 524 Numerical Linear Algebra (3) This course provides a graduate level foundation in numerical linear algebra. It covers the mathematical theory behind numerical algorithms for the solution of linear systems of equations and eigenvalue problems. Specific topics include: matrix decompositions, direct methods of numerical linear algebra, eigenvalue computations, iterative methods.
This course provides an overview of the fundamental concepts of Geometric and Algebraic Topology and presents examples of calculations of principal topological invariants. It starts with review of general topology and covers the following topics: fundamental group, homology theories, index theory, CW complexes, and examples of calculations.
Smooth manifolds, smooth maps, Sard's theorem. The tangent bundle, vector fields, differential forms, integration on manifolds. Foliations. De Rham cohomology; simple applications. Lie groups, smooth actions, quotient spaces, examples. MATH 528 Differentiable Manifolds (3) This course covers the foundations of differential geometry, developing the theory of differentiation and integration on manifolds. It provides tools fo the study of nonlinear problems, combining techniques in analysis and geometry. Concepts and tools from differential geometry have found wide use in different areas of mathematics, including nonlinear differential equations, control and optimization problems, and numerical analysis. The goal is to cover the most important techniques of differential geometry in a concise way. The course will appeal not only to students who plan to do research in geometry, but also to those interested in analysis, or applied and computational mathematics, as well. It covers the following topics: smooth manifolds, smooth maps, Sard’s theorem, the tangent bundle, vector fields, differential forms, integration on manifolds, foliations, de Rham cohomology, Lie groups, smooth actions, quotient spaces, examples.
Manifolds, Poincare duality, vector bundles, Thom isomorphism, characteristic classes, classifying spaces for vector bundles, discussion of bordism, as time allows.
Distributions and Frobenius theorem, curvature of curves and surfaces, Riemannian geometry, connections, curvature, Gauss-Bonnet theorem, geodesic and completeness.
Vector spaces. Linear transformations. Inner products and quadratic forms. Theory of endomorphisms of a finite-dimensional vector space. Orthogonal bases, spectral theorem and applications.
r Groups. Sylow's theorems. Rings. Ideals, unique factorization domains. Finitely generated modules. Fields. Algebraic and transcendental field extensions, Galois theory. MATH 536 Abstract Algebra (3) This course covers fundamental concepts, needed toward the study of advanced areas in abstract algebra. The course covers the following topics: groups, Sylow's theorems, rings, ideals, unique factorization domains, finitely generated modules, fields, algebraic and transcendental field extensions, Galois theory.
Topics selected from Noetherian rings and modules, primary decompositions, Dedekind domains and ideal theory, other special types of commutative rings or fields.
Topics may include algebraic curves, Riemann-Roch theorem, linear systems and divisors, intersectino theory, schemes, sheaf cohomology, algebraic groups.
Solution of linear systems, sparse matrix techniques, linear least squares singular value decomposition, numerical computation of eigenvalues and eigenvectors. Cross-listed with: CSE 550
MATH 551Numerical Solution of Ordinary Differential Equations3
Methods for initial value and boundary value problems; convergence and stability analysis, automatic error control, stiff systems, boundary value problems. Cross-listed with: CSE 551 Graduate - The Pennsylvania State University 2026-2027 1271
MATH 552Numerical Solution Of Partial Differential Equations3
Finite difference methods for elliptic, parabolic, and hyperbolic differential equations; solutions techniques for discretized systems; finite element methods for elliptic problems. Cross-listed with: CSE 552
Interpolation; remainder theory; approximation of functions; error analysis; orthogonal polynomials; approximation of linear functionals; functional analysis applied to numerical analysis.
MATH 401 , 3 credits in Computer Science and Engineering
MATH 555Numerical Optimization Techniques3
Unconstrained and constrained optimization methods, linear and quadratic programming, software issues, ellipsoid and Karmarkar's algorithm, global optimization, parallelism in optimization. Cross-listed with: CSE 555
Sobolev spaces, variational formulations of boundary value problems; piecewise polynomial approximation theory, convergence and stability, special methods and applications. Cross-listed with: CSE 556
, The predicate calculus; completeness and compactness; Godel's first and second incompleteness theorems; introduction to model theory; introduction to proof theory.
Recursive functions; degrees of unsolvability; hyperarithmetic theory; applications to Borel combinatorics. Computational complexity. Combinatory logic and the Lambda calculus.
Dedekind rings; cyclotomic and Kummer extensions; valuations; ramification, decomposition, inertial groups; Galois extensions; locally compact groups of number theory.
This course provides an overview of theory of partitions. This course focuses on the partition function p(n) and its number theoretic behavior and combinatorial structure, along with related problems. To achieve the main goal, generating function theory, basic hypergeometric series, q- series, and some related combinatorial theory are discussed. Building on these relevant theories, students will be able to understand and prove the arithmetic properties of p(n) and related identities including the Rogers- Ramanujan identities. Students will also be able to recognize and apply the same methods to similar functions and identities.
MATH 577Stochastic Systems for Science and Engineering3
The course develops the theory of stochastic processes and linear and nonlinear stochastic differential equations for applications to science and engineering. Cross-listed with: ME 577
Theory and physical interpretation of continuous and discrete wavelet transforms for applications in different engineering disciplines. Cross-listed with: ME 578
A graduate course of fundamental techniques including Ordinary, Partial, and Stochastic Differential Equations, Wavelet Analysis, and Perturbation Theory.
Introduction to mathematical modeling, covering the basic modeling and common mathematical techniques for problems from physical, biological and social sciences.
Complexity of integer multiplication, polynomial multiplication, fast Fourier transform, division, calculating the greatest common divisor of polynomials.
/Maximum of 9 Creative projects, including nonthesis research, which are supervised on an individual basis and which fall outside the scope of formal courses.
/Maximum of 9 Formal courses given on a topical or special interest subject which may be offered infrequently; several different topics may be taught in one year or term.
