# Penn State Mathematics Courses

These are the Penn State mathematics courses that we tutor. If you don't see a course listed in which you need help, e.g. a mathematically intensive course offered at Penn State outside of the Mathematics Department or a course at another school, fill out the consultation request form and provide details of your situation in the area provided for additional information.

In addition to face-to-face tutoring for clients in State College, PA and online tutoring for for clients worldwide,** we offer course materials-practice tests with detailed solution sets and quick reference guides- for Penn State Math 141.** We will be adding more courses to our offerings in the future.

These course materials are distributed through **Nittany Notes**, 139 S. Pugh Street, State College, PA 16801.

Penn State Math 141

Practice Tests, Detailed Solution Sets and Quick Reference Guides

from

Nittany Notes

*Click the course number and name to expand the course description.*

Functions, graphs, derivatives, integrals, techniques of differentiation and integration, exponentials, improper integrals, applications. Students may take only one course for credit from MATH 110, 140, 140A, and 140B.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2013

Prerequisite:MATH 022 or satisfactory performance on the mathematics placement examination

**Note :** Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

Analytic geometry, partial differentiation, maxima and minima, differential equations.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 1988

Prerequisite:
MATH 110

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Functions, limits; analytic geometry; derivatives, differentials, applications; integrals, applications. Students may only take one course for credit from MATH 110, 140, 140A, 140B,140H.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2013

Prerequisite: MATH 022, MATH 026; or MATH 040 or MATh 041 or satisfactory performance on the mathematics placement examination

**Note :** Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

Review of algebra and trigonometry; analytic geometry; functions; limits; derivatives, differentials, applications; integrals, applications. Students may take only one course for credit from MATH 110, 140, 140A, and 140B.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2013

Prerequisite:
satisfactory performance on the mathematics placement examination

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Functions, limits, analytic geometry; derivatives, differentials, applications from biology; integrals, applications from biology. Students may take only one course for credit from MATH 110, 140, 140A, and 140B.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; or MATH 040 or MATH 041 or satisfactory performance on mathematics placement examination

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Functions; limits; analytic geometry; derivatives; differentials, applications; integrals, applications.

MATH 140E enriches the regular MATH 140 syllabus by adding weekly applied problems, a small number of laboratory sessions, and a major group project for which both written and oral presentation is required. It is a rigorous calculus course with additional motivation and applications in the engineering sciences. The core material is the same as MATH 140.

MATH 140E provides an alternative to the regular MATH 140 for engineering majors. This course addresses the additional needs of engineering majors with regard to problem formulation and the interpretation of their mathematical solutions.

The prerequisite for the course is MATH 022, 026; or MATH 040, 041; or satisfactory performance in the mathematics proficiency examination. Six sections of this course are offered every Fall semester.

Course evaluation is based on quizzes, weekly applied problems, two midterms, a group project, and a final examination.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; or MATH 040 or MATH 041 or satisfactory performance in the mathematics placement examination

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Functions, limits, analytic geometry; derivatives, differentials, applications from the earth and mineral sciences; integrals, applications from the earth and mineral sciences. Students may only take one course for credit from MATH 110, 140, 140A, 140B, 140E, and 140G.

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. The typical delivery format for the course is four 50-minute lectures per week, with typical assessment tools including examinations, quizzes, homework, and writing assignments.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; or MATH 040 or MATH 041 or satisfactory performance on the mathematics placement examination

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Honors course in functions, limits; analytic geometry; derivatives, differentials, applications; integrals, applications. Students may only take one course for credit from MATH 110, 140, 140A, 140B, and 140H.

**(BA) This course meets the Bachelor of Arts degree requirements.**

This course is the first in a sequence of three calculus courses designed for students in engineering, science, and related fields. Topics include limits of functions, continuity; the definition of the derivative, various rules for computer 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.

The typical delivery format for the course is four 50-minute lectures per week, with typical assessment tools including examinations, quizzes, homework, and writing assignments.

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.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2013

Prerequisite:
MATH 022, MATH 026 ; or MATH 040 or MATH 041 or satisfactory performance on the mathematics placement examination

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Derivatives, integrals, applications; sequences and series; analytic geometry; polar coordinates. Students may take only one course for credit from MATH 141, 141B, and 141H.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1996

Prerequisite:
MATH 140,MATH 140A ,MATH 140B or MATH 140H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Derivatives, integrals, applications from biology; sequences and series; analytic geometry; polar coordinates. Students may take only one course for credit from MATH 141 and 141B.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1996

Prerequisite:
MATH 140B

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Integration, applications; sequences and series; parametric equations, application.

MATH 141E enriches the regular MATH 141 syllabus by adding weekly applied problems, a small number of laboratory sessions, and a major group project for which both written and oral presentations are required. It is a rigorous calculus course with additional motivation and applications in the engineering sciences, designed to enhance the student's problem solving skills and their understanding of how calculus is applied to real world problems. The core material is the same as MATH 141.

MATH 141E provides an alternative to the regular MATH 141 for engineering majors. This course addresses the additional needs of engineering majors with regard to problem formulation and the interpretation of their mathematical solutions.

The prerequisite of the course is MATH 140, 140A, 140B, or 140E; or the consent of the instructor. Six sections of this course are offered every Spring semester.

Course evaluation is based on quizzes, weekly applied problems, two midterms, a group project, and a final examination.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 2001

Prerequisite:
MATH 140, MATH 140A,MATH 140B or MATH 140E

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Derivatives, integrals, applications from the earth and mineral sciences; sequences and series; analytic geometry; polar coordinates. Students may take only one course for credit from MATH 141, 141B, 141E, and 141G.

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; parametric equations and polar coordinates.

The typical delivery format of the course is four 50-minute lectures per week, with typical assessment tools including examinations, quizzes, homework, and writing assignments.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2005

Prerequisite:
MATH 140, MATH 140A, MATH 140B, MATH 140E or MATH 140G

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Honors course in derivatives, integrals, applications; sequences and series; analytic geometry; polar coordinates. Students may take only one course for credit from MATH 141, 141B, and 141H.

**(BA) This course meets the Bachelor of Arts degree requirements.**

This course is the second in a sequence of three calculus courses designed for students in engineering, science, 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; parametric equations and polar coordinates.

The typical delivery format for the course is four 50-minute lectures per week, with typical assessment tools including examinations, quizzes, homework, and writing assignments.

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.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2006

Prerequisite:
MATH 140, MATH 140A, MATH 140B or MATH 140H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Systems of linear equations; matrix algebra; eigenvalues and eigenvectors; linear systems of differential equations.

**(BA) This course meets the Bachelor of Arts degree requirements.**

Systems of linear equations appear everywhere in mathematics and its applications. MATH 220 will give students the basic tools necessary to analyze and understand such systems.

The initial portion of the course teaches the fundamentals of solving linear systems. This requires the language and notation of matrices and fundamental techniques for working with matrices such as row and column operations, echelon form, and invertibility. The determinant of a matrix is also introduced; it gives a test for invertibility.

In the second part of the course the key ideas of eigenvector and eigenvalue are developed. These allow one to analyze a complicated matrix problem into simpler components and appear in many disguises in physical problems. The course also introduces the concept of a vector space, a crucial element in future linear algebra courses.

This course is completed by a wide variety of students across the university, including students majoring in engineering programs, the sciences, and mathematics. (In case of many of these students, MATH 220 is a required course in their degree program.)

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2009

Prerequisite:
MATH 110, MATH 140 or MATH 140H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Honors course in systems of linear equations; matrix algebra; eigenvalues and eigenvectors; linear systems of differential equations.

**(BA) This course meets the Bachelor of Arts degree requirements.**

This course is intended as an introduction to linear algebra with a focus on solving systems for linear equations. Topics include systems of linear equations, row reduction and echelon forms, linear independence, introduction to linear transformations, matrix operations, inverse matrices, dimension and rank, determinants, eigenvalues, eigenvectors, diagonalization, and orthogonality.

The typical delivery format for the course is two 50-minute lectures per week, with typical assessment tools including examinations, quizzes, homework, and writing assignments.

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.

General Education: GQ

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2009

Prerequisite:
MATH 110, MATH 140 or MATH 140H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Three-dimensional analytic geometry; vectors in space; partial differentiation; double and triple integrals; integral vector calculus. Students who have passed either Math 231 or 232 may not schedule Math 230 or 230H for credit.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1996

Prerequisite:
MATH 141 or MATH 141H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

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 232 may not schedule MATH 230 or 230H for credit.

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; double integrals, triple integrals; line integrals, Green's Theorem, Stokes' Theorem, the Divergence Theorem.

The typical delivery format for the course is four 50-minute lectures per week, with typical assessment tools including examinations, quizzes, homework, and writing assignments.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2006

Prerequisite:
MATH 141 or MATH 141H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Analytic geometry in space; partial differentiation and applications. Students who have passed MATH 230 or MATH 230H may not schedule this course.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1996

Prerequisite:
MATH 141 or MATH 141H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Honors course in analytic geometry in space; partial differentiation and applications. Students who have passed MATH 230 or MATH 230H may not schedule this course.

This course covers a subset of the material found in MATH 230. 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.

The typical delivery format for the course is two 50-minute lectures per week, with typical assessment tools including examinations, quizzes, homework, and writing assignments.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2006

Prerequisite:
MATH 141 or MATH 141H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

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.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1996

Prerequisite:
MATH 231

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

First- and second-order equations; special functions; Laplace transform solutions; higher order equations. Students who have passed MATH 251 may not schedule this course for credit.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1988

Prerequisite:
MATH 141

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

First- and second-order equations; special functions; Laplace transform solutions; higher order equations; Fourier series; partial differential equations.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1988

Prerequisite:
MATH 141 or MATH 141H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Honors course in first- and second-order equations; special functions; Laplace transform solutions; higher order equations; Fourier series; partial differential equations.

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.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2006

Prerequisite:
MATH 141 or MATH 141H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Fundamental techniques of enumeration and construction of combinatorial structures, permutations, recurrences, inclusion-exclusion, permanents, 0, 1- matrices, Latin squares, combinatorial designs.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1985

Prerequisite:
MATH 220

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Honors version of elementary and enumerative combinatorics.

Math 310 introduces students to the fundamental techniques (i.e., addition, subtraction, multiplication, and division) and structures (i.e., permutations and combinations) of counting. An emphasis is placed on understanding the combinatorial interpretations of these objects and usin these interpretations to prove various identities (as opposed to using mathematical induction). By the end of the semester, the successful student will be able to apply these methods to a complete set of distribution problems (distributing distinct/identical objects to distinct/identical boxes).

While Math 310H will introduce the student to the same fundamental techniques and structures, more of an emphasis will be placed on a variety

of different counting techniques. Students will be exposed to the principle of inclusion-exclusion, the transfer-matrix method, bijective proofs, and see a much more in-depth treatment of generating functions. The successful student will be able to apply these techniques to a much
broader spectrum of combinatorial problems than what is seen in Math 310.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2012

Prerequisite:
MATH 220

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Basic methods of mathematical thinking and fundamental mathematical structures, primarily in the context of numbers, groups, and symmetries.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2006

Prerequisite:
MATH 141

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Introduction to mathematical proofs; elementary number theory and group theory. Students who have passed CMPSC 360 may not schedule this course for credit.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2007

Prerequisite:
MATH 141

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

An introduction to rigorous analytic proofs involving properties of real numbers, continuity, differentiation, integration, and infinite sequences and series.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1994

Prerequisite:
MATH 141

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Basic methods of mathematical thinking and fundamental structures, primarily in the context of infinite sets, real numbers, and metric spaces.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 2006

Prerequisite:
MATH 141

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Combinatorial analysis, axioms of probability, conditional probability and 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.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1989

Prerequisite:
MATH 141

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Statistical inference: principles and methods, estimation and testing hypotheses, regression and correlation analysis, analysis of variance, computer analysis. Students who have passed MATH(STAT) 415 may not schedule this course for credit.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1989

Prerequisite:
MATH 318 or knowledge of basic probability

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Review of calculus, properties of real numbers, infinite series, uniform convergence, power series. Students who have passed Math. 403 may not schedule this course.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1983

Prerequisite:
MATH 230 or MATH 231

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Topology of R^{n}, compactness, continuity of functions, uniform convergence, Arzela-Ascoli theorem in the plane, Stone-Wierstrass theorem.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1996

Prerequisite:
MATH 312

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Development of a thorough understanding and technical mastery of foundations of classical analysis in the framework of metric spaces.

The central aim of this course is to develop thorough understanding and technical mastery of foundations of classical analysis in the framework of metric spaces rather than multidimensional Euclidean spaces. This level of abstraction is essential since it is in the background of functional analysis, a fundamental tool for modern mathematics and physics. Another motivation for studying analysis in this wider context is that many general results about functions of one or several real variables are more easily grasped at this more abstract level, and, besides, the same methods and techniques are applicable to a wider class of problems, e.g. to the study of function spaces. This approach also brings to high relief some of the fundamental connections between analysis on one hand and (higher) algebra and geometry on the other.

This course is a sequel to Math 312H; 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: Metric spaces (topology, convergence, Cauchy sequences and completeness); Maps between metric spaces (continuous maps and
homeomorphisms, stronger continuity properties:

uniform continuity, Hoelder and Lipschitz continuity, contraction mapping principle, points of discontinuity and the Baire Category Theorem); Compact metric spaces (continuity and compactness, connectedness, total boundedness, coverings and Lebesgue number, perfect metric spaces, characterization of Cantor sets, fractals); Function spaces (spaces of continuous maps, uniform continuity and equicontinuity,

Arzela-Ascoli Theorem, uniform approximation by polynomials. Stone-Weierstrass Theorem).

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2010

Prerequisite:
MATH 311M, MATH 312H

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Differentiation of functions from Rn to Rm, implicit function theorem, Riemann integration, Fubini's theorem, Fourier analysis.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1985

Prerequisite:
MATH 403

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Vector calculus, linear algebra, ordinary and partial differential equatinos. Students who have passed MATH 411 or 412 may not take this course for credit.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1994

Prerequisite:
MATH 231; MATH 250 or MATH 251

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Complex analytic functions, sequences and series, residues, Fourier and Laplace transforms. Students who have passed MATH 421 may not take this course for credit.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1994

Prerequisite:
MATH 405

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Differential and integral calculus of functions of several variables, line and surface integrals, infinite series, series of functions, power series.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2007

Prerequisite:
MATH 141

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Complex analytic functions; Cauchy-Riemann equations; complex contour integrals; Cauchy's integral formula; Taylor and Laurent series; residue theory; applications in engineering.

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.

General Education: None

Diversity: None

Bachelor of Arts: None

Effective: Summer 2014

Prerequisite:
MATH 230 or MATH 232

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Linear ordinary differential equations; existence and uniqueness questions; series solutions; special functions; eigenvalue problems; Laplace transforms; additional topics and applications.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1983

Prerequisite:
MATH 230 or MATH 231 ; MATH 250 or MATH 251

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Orthogonal systems and Fourier series; derivation and classification of partial differential equations; eigenvalue function method and its applications; additional topics.

**(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.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2009

Prerequisite:
MATH 230; MATH 250 or MATH 251

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

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 MATH(STAT) 414 and 418 for credit.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 2001

Prerequisite:
MATH 230 or MATH 231

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

A theoretical treatment of statistical inference, including sufficiency, estimation, testing, regression, analysis of variance, and chi-square tests.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1989

Prerequisite:
MATH 414

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Review of distribution models, probability generating functions, transforms, convolutions, Markov chains, equilibrium distributions, Poisson process, birth and death processes, estimation.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1984

Prerequisite:
MATH 318 or MATH 414; MATH 230

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Linear differential equations, stability of stationary solutions, ordinary bifurcation, exchange of stability, Hopf bifurcation, stability of periodic solutions, applications.

**(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.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2009

Prerequisite:
MATH 220; MATH 250 or MATH 251

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Introduction to probability axioms, combinatorics, random variables, limit laws, and stochastic processes. Students may take only one course from MATH(STAT) 414 and 418 for credit.

This course gives an introduction to probability and random processes. The topics are not covered as deeply as in a semester-long course in probability only or in a semester-long course in stochastic processes only. It is intended as a service course primarily for engineering students, though no engineering background is required or assumed.

The topics covered include probability axioms, conditional probability, and combinatorics; discrete random variables; random variables with continuous distributions; jointly distributed random variables and random vectors; sums of random variables and moment generating functions; and stochastic processes, including Poisson, Brownian motion, and Gaussian processes.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 2011

Prerequisite:
MATH 230 or MATH 231

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Principles of Newtonian, Lagrangian, and Hamiltonian mechanics of particles with applications to vibrations, rotations, orbital motion, and collisions.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2007

Prerequisite:
MATH 230 or MATH 231; MATH 250 or MATH 251 ; PHYS 212, PHYS 213 and PHYS 214

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Infinite sequences and series; algebra and geometry of complex numbers; analytic functions; integration; power series; residue calculus; conformal mapping, applications.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Summer 1993

Prerequisite:
MATH 230 , MATH 232 or MATH 405; MATH 401 or MATH 403

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Euclidean and various non-Euclidean geometries and their development from postulate systems. Students who have passed MATH 427 may not schedule MATH 471.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1994

Prerequisite:
MATH 230 or MATH 231

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Metric spaces, topological spaces, separation axioms, product spaces, identificaiton spaces, compactness, connectedness, fundamental group.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 1994

Prerequisite:
MATH 311W

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Elementary theory of groups, rings, and fields. Students who have passed MATH 435 may not schedule MATH 470.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2010

Prerequisite:
MATH 311W or MATH 315

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Vector spaces and linear transformations, canonical forms of matrices, elementary divisors, invariant factors; applications. Students who have passed MATH 436 may not schedule MATH 441.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1983

Prerequisite:
MATH 311W

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Determinants, matrices, linear equations, characteristic roots, quadratic forms, vector spaces. Students who have passed Math 436 may not schedule this course.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1985

Prerequisite:
MATH 220

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Constructing mathematical models of physical phenomena; topics include pendulum motion, polymer fluids, chemical reactions, waves, flight, and chaos.

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 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.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2007

Prerequisite:
MATH 315 and MATH 430 or MATH 405 or MATH 412

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Algorithms for interpolation, approximation, integration, nonlinear equations, linear systems, fast FOURIER transform, and differential equations emphasizing computational properties and implementation. Students may take only one course for credit from MATH 451 and 455.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Spring 2008

Prerequisite:
3 credits of programming; MATH 230 or MATH 231

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Continuation of Math.(Phys.) 419. Theoretical treatment of dynamics of a rigid body, theory of elasticity, aggregates of particles, wave motion, mechanics of fluids.

General Education: None

Diversity: None

Bachelor of Arts: Quantification

Effective: Fall 1986

Prerequisite:
MATH 419

**Note :** Class size, frequency of offering, and evaluation methods will vary by
location and instructor. For these details check the specific course syllabus.

Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics.

General Education: None

Diversity: None

Bachelor of Arts: None

Effective: Summer 2000

Prerequisite:
MATH 403

**Note :** Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics.

General Education: None

Diversity: None

Bachelor of Arts: None

Effective: Summer 2000

Prerequisite:
MATH 403

**Note :** Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.