Courses

Undergraduate Courses in
the Department of Mathematics and Statistics

This list contains, for each course, its official catalog description, followed by informal comments about it, including the usual clientele, the current textbook, and how frequently it is offered. For up-to-date class schedule information, as well as other general information, go to the Oakland University home page and click on the SAIL icon, or follow this link for tentative schedules of courses offered by the Department of Mathematics and Statistics for upcoming terms.

The comments below other than the official catalog copy are the advice and opinion of Professor Grossman, departmental academic adviser, and should not be viewed as official department policy. Please check with a course's instructor in a given term or with an adviser in the department for further details (in particular, instructors sometimes have web pages for their courses with more information; see the faculty list for faculty members' home pages).

Courses must be passed with a grade of 2.0 (C) or better in order to satisfy prerequisites.

Almost all courses are 4-credits, the main exceptions being MTH 256 and APM 257, each of which is 3 credits (although these courses were replaced by 4-credit courses during 2005-2007), and independent study or topics courses (which are usually 2 or 4 credits). The rubrics MTH, APM, STA, MOR, and MTE indicate the kind of course: MTH for pure mathematics as well as introductory courses, APM for applied mathematics, STA for statistics, MOR for operations research, and MTE for courses designed for elementary education majors. These categories are not rigid, however, and should not be taken literally.

MTH: MATHEMATICS

MTH 011 Elementary Algebra (4 credits)

Order of operations, algebra of exponents, radicals, variable expressions, polynomial arithmetic, factoring algebraic fractions, linear equations and inequalities in one variable; applications and problem solving. This course cannot be used to satisfy minimal graduation requirements in any program.
Prerequisite: none.
[MTH 011 covers approximately the first half of the textbook Beginning and Intermediate Algebra by Gustafson and Frisk (while MTH 012 covers most of the second half), and it is offered every fall and winter (including an evening section in the fall). This course assumes no prior knowledge of algebra. Students who have scored well on the mathematics portion of the ACT test (the current cut-off is 18 or higher) are considered to have placed out of MTH 011; students who have not taken the ACT should take the placement exam before registering for this course to determine whether they have enough background to skip it and start in a higher level course. Students who seriously studied and mastered three years of college preparatory mathematics from a good high school should be able to place out of MTH 011-012. On the other hand, if you feel that you need a review before going on to more advanced courses, then you may opt to take this course even if you have placed out of it.]

MTH 012 Intermediate Algebra (4 credits)

Complex numbers, quadratic equations, nonlinear inequalities, analytic geometry (points and lines in the coordinate plane, distance, circles, parabolas, ellipses and hyperbolas), 2 by 2 and 3 by 3 systems of linear equations, introduction to functions and their graphs, theory of equations, logarithms; applications and problem solving. This course cannot be used to satisfy minimal graduation requirements in any program.
Prerequisite: MTH 011 or placement.
[MTH 012 covers most of the second half of the textbook Beginning and Intermediate Algebra by Gustafson and Frisk (while MTH 011 covers approximately the first half), and it is offered in numerous day and evening sections every fall and winter (and usually also in the spring). Students who have scored well on the mathematics portion of the ACT test (the current cut-off is 18 or higher) are considered to have placed out of MTH 011; students who have not taken the ACT (or already passed an elementary algebra course with a C or better) must take the placement exam before registering for MTH 012 to determine whether they have the necessary background for it or whether they need to start in MTH 011. (On the other hand, if your ACT math score is 22 or higher, or if you do very well on the placement test, then you can skip MTH 012.) Students who seriously studied and mastered three years of college preparatory mathematics from a good high school should be able to place out of MTH 011-012. See also MTH 052 below.]

MTH 052 Intermediate Algebra Workshop (2 credits)

Students work cooperatively in groups to solve challenging problems based on the mathematics in MTH 012. The students will learn computational and theoretical mathematics taught through discovery rather than by lecture. Open only to students concurrently enrolled in MTH 012.
Corequisite: MTH 012.
[This is an optional supplement to MTH 012 and recommended for improving the student's success in this and subsequent mathematics courses. Usually offered fall and winter.]

MTH 100 Topics in Elementary Mathematics (2 or 4 credits)

A selection of topics designed to develop student awareness and appreciation of mathematics with an emphasis on problem solving. Developed to support the transition of students into the university mathematical sciences curriculum.
Prerequisite: Placement by the Student Success Services office only.
[This course last used the textbook Introductory Algebra, an Applied Approach by Aufmann, Barker, and Lockwood and emphasized algebraic skills and problem solving. It was offered in the summer only for students in a summer institute run by the Student Success Services office, to be completed in the summer or extended into the fall. Upon successful completion of this course, most students were ready for MTH 012 or MTH 118. The course was graded S/U and offered for 4 credits only. The program has been suspended, however, and the course is no longer offered.]

MTH 118 Mathematical Sciences in the Modern World (4 credits)

Designed for students without an extensive mathematics background who wish to explore the ways people use mathematical sciences to solve problems that arise in modern society. Satisfies the university general education requirement in mathematics, logic and computer science. Formerly called MTH 185.
Prerequisite: none.
[This course currently uses the textbook Excursions in Modern Mathematics by Tannenbaum. It is an excellent course for learning about very interesting applications of mathematics to such problems as voting. It is a good choice for elementary education mathematics majors and minors, as well as majors in the humanities and social sciences. One section of this course is usually offered fall and winter.]

MTH 121 Linear Programming, Elementary Functions (4 credits)

Systems of equations, matrices, and linear programming (simplex method); rational, exponential and logarithmic functions. Satisfies the university general education requirement in mathematics, logic and computer science.
Prerequisite: MTH 012 or placement.
[This course currently uses the textbook Finite Mathematics and Applied Calculus by Waner and Costenoble. The official course description omits one other topic covered briefly in this course: financial mathematics (compound interest and annuities). About half the course time is devoted to matrices and linear programming, and most of the rest is really a college algebra course to prepare students for calculus (MTH 122). The emphasis is on modeling using mathematics, and usually group projects are required. This course is aimed almost entirely at students in the School of Business Administration, for whom it is required. It is not a good choice for any other students. Students need the algebraic skills at the level of MTH 012 in order to succeed in this course. This course is usually offered in numerous sections (day and evening) in fall and winter, as well as in spring and summer.]

MTH 122 Calculus for the Social Sciences (4 credits)

The basic concepts, theorems and applications to the social sciences of the differential and integral calculus of one and several variables. Satisfies the university general education requirement in mathematics, logic and computer science.
Prerequisite: MTH 121 or MTH 141 or placement.
[This course currently uses the textbook Finite Mathematics and Applied Calculus by Waner and Costenoble.] It is the second half of the MTH 121-122 sequence taken by students in SBA (see above), but it is also appropriate for students in biology, health sciences, elementary education, and other areas who wish to learn something about calculus. This course is much less rigorous than MTH 154, with the emphasis not so much on physics and engineering examples; furthermore, it covers (again, at a lower level) some of the topics in MTH 155 and MTH 254. This course assumes algebraic skills at the level of MTH 121 or MTH 141, and students lacking those skills are unlikely to succeed in MTH 122. This course is usually offered in numerous sections (day and evening) in fall and winter, as well as in spring and summer.]

MTH 141 Precalculus (4 credits)

Functions, roots of polynomials, rational, exponential and logarithmic functions, trigonometric functions (including graphs, identities, inverse functions, equations and applications), complex numbers, analytic geometry and conic sections.
Prerequisite: MTH 012 or placement.
[This course currently uses the textbook Precalculus by Cohen. It could be called College Algebra and Trigonometry (about half the course for each of theses areas), and its primary purpose is to cover the knowledge, understanding, and skill base needed for the study of calculus. This course is much more difficult than most students are used to from high school or from MTH 012. Algebra knowledge at the MTH 012 level is assumed and is a very necessary prerequisite. Students who seriously studied and mastered four years of college preparatory mathematics from a good high school should be able to place out of MTH 141. A graphing calculator such as the TI-83 will be a valuable tool for students in this course. The course does not satisfy the general education requirement, because it does not meet the goals of that program and duplicates high school material. The course is appropriate for students in the sciences, health sciences, elementary education, and anyone who plans to study more advanced mathematics. We offer this course fall and winter both in traditional day and evening sections and in a four-day-a-week lecture/recitation format; a section is usually offered in the spring term as well. See also MTH 142 below.]

MTH 142 Precalculus Workshop (2 credits)

Students work cooperatively in groups to solve challenging problems based on the mathematics in MTH 141. The students will learn computational and theoretical mathematics taught through discovery rather than by lecture. Open only to students concurrently enrolled in MTH 141.
Corequisite: MTH 141.
[This is an optional supplement to MTH 141 and recommended for improving the student's success in this and subsequent mathematics courses. Usually offered fall and winter.]

MTH 154 Calculus I (4 credits)

[catalog description for MTH 154-155 together:] A comprehensive study of analytic geometry, limits, differentiation and integration of functions of one real variable, including transcendental functions, infinite series, indeterminate forms, polar coordinates, numerical methods and applications. Each is offered fall and winter semester. Satisfies the university general education requirement in mathematics, logic and computer science.
Prerequisite: MTH 141 or placement.
[This course currently uses the textbook Calculus with Early Transcendentals by Stewart. It is the standard first semester calculus course taken by majors in engineering, computer science, the physical sciences, mathematics, statistics, and perhaps a few others. Students must understand the contents of MTH 141 very well in order to succeed in this course, particularly the notion of function and graphs of functions. Of course algebraic skills must also be under one's belt before taking this course. A graphing calculator such as the TI-83 is highly recommended. Students are also encouraged to make use of computer algebra packages such as Maple or Mathematica (or what is available on a calculator such as the TI-89) while studying calculus. We are currently experimenting with aspects of the course to improve students' success and retention of what they learn; this might include some non-calculator exams and some outside-of-class group projects. There are both day and evening sections fall and winter, and usually one section in the summer term.]

MTH 155 Calculus II (4 credits)

MTH 254 Multivariable Calculus (4 credits)

A study of vectors, polar coordinates, three-dimensional geometry, differential calculus of functions of several variables, exact differential equations, multiple integrals, line and surface integrals, and vector fields.
Prerequisite: MTH 155.
[This course currently continues with the textbook used in MTH 154-155. In some sense this is just a continuation of MTH 154-155, but not everyone listed above as taking the first two terms is required to take this course. Otherwise, most of the comments under MTH 154 apply. There are both day and evening sections fall and winter.]

MTH 256 Introduction to Linear Algebra (3 credits)

An introduction to the theoretical and computational aspects of linear algebra. Topics covered include linear equations, vectors and matrices, matrix algebra, determinants, eigenvalues and eigenvectors, linear transformations, vector spaces and inner product spaces.
Prerequisite: MTH 155.
[This course currently uses the textbook Linear Algebra by Poole. The course is required of majors in mathematics, statistics, engineering, and computer science. An optional 1-credit laboratory course, MTH 266 (see below), is offered in conjunction with this course. Students who can fit it into their programs will benefit by taking the lab concurrently with the course, or the lab can also be taken subsequently. The point of the calculus prerequisite is not that calculus is used heavily in this course, but rather that the student needs a certain amount of mathematical maturity in order to handle the abstractions of this course, and one usually gains that maturity after a year-long study of calculus. Students are expected to understand the proofs of some theorems in this course, and occasionally to prove things themselves. One CS major commented that he thought it would be wise to take APM 263 (Discrete Mathematics, a required course for the CS major) before taking MTH 256 for this reason, but this is certainly not a requirement. There are both day and evening sections of MTH 256 in fall and winter, and often one section in the summer. During 2005-2007, this course is gradually being replaced by a 4-credit linear algebra course with more emphasis on theory, to be called MTH 275. Engineering students will no longer take a separate linear algebra course but will learn the subject in the context of a new 4-credit differential equations course.]

MTH 266 Linear Algebra Laboratory (1 credit)

Computational investigation of selected topics in linear algebra.
Corequisite: MTH 256.
[This laboratory is a useful supplement to MTH 256 for those students who can fit it in. It is currently run via the Internet and uses computer software selected by the instructor. It may be taken concurrently with or subsequent to MTH 256. This course will probably be phased out with MTH 256.]

MTH 275 Linear Algebra (4 credits

Study of general vector spaces, linear systems of equations, linear transformations and compositions, eigenvalues and eigenvectors, diagonalization, modeling and orthogonality. Provides a transition to formal mathematics.
Prerequisite: MTH 155.
[This course currently uses the textbook Linear Algebra by Poole. The course is required of majors in mathematics, statistics, and computer science. An optional 1-credit laboratory course, MTH 266, is offered in conjunction with this course. Students who can fit it into their programs will benefit by taking the lab concurrently with the course, or the lab can also be taken subsequently. The point of the calculus prerequisite is not that calculus is used heavily in this course, but rather that the student needs a certain amount of mathematical maturity in order to handle the abstractions of this course, and one usually gains that maturity after a year-long study of calculus. Students are expected to understand the proofs of some theorems in this course, and occasionally to prove things themselves. There are both day and evening sections of MTH 256 in fall and winter, and often one section in the summer. This course replaces MTH 256.]

MTH 290 Independent Study (2 or 4 credits)

Reading or research on some mathematical topic. May be repeated for additional credit.
Prerequisite: Permission of department.
[As the title indicates, a student takes this course on his/her own, rather than in a class. The subject matter can be anything that the student and the supervisor agree on, although usually independent study is not given in subjects regularly offered as courses. The format is also up to the participants, and can range from reading, oral reports, written reports, homework exercises to assisting a professor in a research project. Independent study at the freshman/sophomore level should be taken as MTH 290; for more advanced students, projects in pure mathematics should be given as MTH 490, projects in applied mathematics as APM 490, and projects in statistics as STA 490. Independent study is available during every term. Before registering for this course, of course, the student must make arrangements with a faculty member, and the two people involved should spell out what will be done, using a form supplied by the department.]

MTH 302 Introduction to Advanced Mathematical Thinking (4 credits)

The propositional and predicate calculus, set theory, methods of mathematical proof, inductive and recursive thinking, relations and functions, infinity. Emphasis is on rigorous proofs of mathematical statements.
Prerequisite: MTH 256 or APM 263 permission of department.
[This course currently uses the textbook Transition to Advanced Mathematics by Smith; it has sometimes used A Transition to Advanced Mathematics by Chartrand, Polimeni, and Zhang. This is an extremely important course, required of all mathematics majors and secondary education mathematics minors. Advanced mathematics is concerned with why mathematical truths are true, rather than solely with solving problems. In this course, the student will learn how to read, understand, and construct proofs of mathematical statements. The course is prerequisite for many advanced courses, such as MTH 452 and MTH 475. The prerequisite of APM 263 or MTH 275 (or 256) insures that the student has reached the appropriate point in his or her mathematical development to be able to understand the material being presented. The first several weeks of APM 263 also concern themselves with logic, sets, and proofs. MTH 302 is offered in the fall term only, usually in the late afternoon.]

MTH 452 Advanced Calculus I (4 credits)

The topology of the real number line and of n-dimensional Euclidean space, continuity and uniform continuity, derivatives, the Riemann integral, sequences and series, uniform convergence. [Renumbering of MTH 351.] Offered every fall.
Prerequisite: MTH 254 and MTH 302 or permission of department.
[This course uses a textbook selected by the instructor, such as An Introduction to Analysis by Wade, or Advanced Calculus by Buck. It is required of all mathematics majors. The subject matter is similar to the material of the calculus sequence (MTH 154-155-254), but now the emphasis is more on the theory and subtleties of what's going on, rather than doing calculations or getting answers to problems. Proofs are stressed, so the MTH 302 prerequisite is very important. This course is offered every fall, in a late afternoon time slot. Students who wish to obtain the B.S. degree must complete the sequel, MTH 453.]

MTH 352 Complex Variables (4 credits)

A study of analytic functions of a complex variable including differentiation and integration, series representations, the theory of residues and applications.
Prerequisite: MTH 254.
[This course is offered about once every two years.]

MTH 462 Geometric Structures (4 credits)

A study of topics from Euclidean geometry, projective geometry, non-Euclidean geometry and transformation geometry. [Renumbering of MTH 361.] Offered every fall.
Pre- or corequisite: MTH 302 or permission of department.
[This course currently uses Road to Geometry by Wallace. Click here for the web site for the course in Fall 1998. The course also used The Geometer's Sketchpad software. MTH 462 is a required elective for students in the secondary education program (STEP), and is also required for mathematics minors in that program. The course is usually offered in the late afternoons two days a week, fall semester.]

MTH 472 Number Theory with Cryptography (4 credits)

Structure of the integers, prime factorization, congruences, multiplicative functions, primitive roots and quadratic reciprocity, and selected applications including cryptography. [Renumbering of MTH 372.]
Prerequisite: MTH 155.
[This course currently uses the textbook Elementary Number Theory and Its Applications by Rosen, and is offered about once every two years. It is an excellent choice for students in the secondary education program (STEP) as well as for computer science majors. Both the theoretical aspects of the subject and modern applications, such as to cryptography, as studied, and often computer assignments are a major part of the course.]

MTH 405 Special Topics (2 or 4 credits)

Advanced study of a selected topic in mathematics. May be repeated for additional credit.
Prerequisite: Permission of instructor.
[When a faculty member wishes to offer a course on a topic not otherwise represented in the catalog, this number is used. Interested students should talk to the faculty member teaching the course for all relevant information.]

MTH 414 History of Mathematics (4 credits)

Mathematics from ancient to modern times, its growth, development and place in human culture. Offered every winter.
Prerequisite: MTH 351 or permission of instructor.
[This is a good capstone course to take during one's last semester at the university, and it is a required course for students in the secondary education program (STEP). A recent offering used A History of Mathematics by Boyer and Merzbach; sometimes in the past it was a history of the development of calculus using original sources (the emphasis varies with the instructor).]

MTH 415 Foundations of Mathematics: Mathematical Logic and Set Theory (4 credits)

An examination of the logical foundations of mathematics including analysis of the axiomatic method, basic set theory, cardinal and ordinal numbers, and the axiom of choice.
Prerequisite: MTH 302.
[This course is offered about once every two or three years. As well as being a course in mathematics, it is a course about mathematics -- it studies the issues of proof and truth of mathematical statements, and in particular looks at set theory as a unifying theme.]

MTH 453 Advanced Calculus II (4 credits)

Improper integrals, derivatives and integrals in n-dimensional Euclidean space, implicit and inverse function theorems, differential geometry and vector calculus, and Fourier series. Offered every winter.
Prerequisite: MTH 351.
[This course is the continuation of MTH 452 (see above). The course is required of B.S. mathematics majors.]

MTH 461 General Topology (4 credits)

A study of topological spaces and continuous functions. Separation and countability properties, connectedness, compactness and local properties.
Prerequisite: MTH 302.
[This course is rarely offered as a formal class, and students interested in studying this fascinating subject (in some sense it's a cross between geometry and advanced calculus) should speak to an adviser or interested faculty member about getting it on the schedule (or take it as an independent study).]

MTH 465 Differential Geometry (4 credits)

Theory of curves and surfaces in Euclidean space with an introduction to the theory of matrix Lie groups.
Prerequisite: MTH 453.
[This course is rarely offered as a class. The subject matter is relevant to computer graphics.]

MTH 475 Abstract Algebra (4 credits)

Groups, subgroups, cosets, and homomorphisms; rings and ideals; integral domains; and field and field extensions. Applications. Offered every winter.
Prerequisite: MTH 302 or permission of department.
[This course uses a textbook such as A First Course in Abstract Algebra by Rotman. It is required of all mathematics majors. The subject matter is hard to describe for someone who hasn't yet studied it, but if you liked the more abstract aspects of MTH 275, you'll probably like MTH 475. The course is offered in a late afternoon or evening time slot in the winter semester.]

MTH 490 Independent Study (2 or 4 credits)

MTH 497 Apprentice College Teaching (2 or 4 credits)

Open to any well-qualified junior or senior who obtains consent of a faculty member to assist in presenting a regular college course. The apprentice should be capable of assuming limited classroom teaching duties. May be repeated for additional credit. Graded S/U.
Prerequisite: Permission of department.
[Although this course is on the books, it has not been used for years. If we ever move to a system of having undergraduate teaching assistants in our courses, this course would enable the participants to get college credit for their efforts.]

APM: APPLICABLE ANALYSIS AND MATHEMATICAL MODELING

APM 163 Mathematics for Information Technology (4 credits)

Systems of linear equations, matrix algebra and linear transformations. Elementary combinatorics, recursion and induction, sets and relations. Enrollment is limited to students in the Bachelor of Science in Information Technology program or with department permission. APM 163 cannot be used to replace APM 263 or MTH 256 or MTH 275. Satisfies the university general education requirement in the knowledge application integration area. Prerequisite for knowledge applications integration: Completion of the general education requirement in the formal reasoning knowledge foundation area or in the natural science and technology knowledge exploration area.
Prerequisite: MTH 122 with at least a 3.0, or MTH 154.
[This course currently uses the textbook Essential Discrete Mathematics by Feil. It is required of students in the Information Technology program.]

APM 255 Introduction to Differential Equations with Matrix Algebra (4 credits)

Introduction to ordinary differential equations, Laplace transforms, linear systems, matrices, vectors, indepedence, eigenvalues and eigenvectors, and applications. [Replaces APM 257, with some of MTH 256 mixed in.]
Prerequisite: MTH 155.
[This course currently uses the textbook Differential Equations and Linear Algebra by Edwards. It is required of students in engineering and physics, and is an elective for mathematics or statistics majors. At least one section is offered in each of fall and winter semesters (one of these in the evening), and it is usually offered in the spring term as well. The most important part of the prerequisite is a good understanding of the meaning of derivative and the integration process. A graphing calculator such as the TI-86 is a useful tool for this course, and students can also make use of computer algebra packages such as Maple or Mathematica.]

APM 257 Introduction to Differential Equations (3 credits)

An introduction to the basic methods of solving ordinary differential equations, including the methods of undetermined coefficients, variations of parameters, series, Laplace transforms and numerical methods. Separable, exact and linear equations. Applications.
Prerequisite: MTH 155.
[This course currently uses the textbook Elementary Differential Equations and Boundary Value Problems by Boyce and DiPrima. It is required of many students in engineering and physics, and is an elective for mathematics or statistics majors. At least one section is offered in each of fall and winter semesters (one of these in the evening), and it is usually offered in the spring term as well. The most important part of the prerequisite is a good understanding of the meaning of derivative and the integration process. A graphing calculator such as the TI-86 is a useful tool for this course, and students can also make use of computer algebra packages such as Maple or Mathematica. This course is being replaced, gradually during the 2005-2007 academic year, by APM 255, a 4-credit course covering both differential equations and a little bit of linear algebra.]

APM 263 Discrete Mathematics (4 credits)

Concepts and methods of discrete mathematics with an emphasis on their application to computer science. Logic and proofs, sets and relations, algorithms, induction and recursion, combinatorics, graphs and trees.
Prerequisite: MTH 155.
[This course currently uses the textbook Discrete Mathematics: An Introduction to Concepts, Methods, and Applications by Grossman. It is required of computer science and computer engineering majors, and is a good choice as an elective for mathematics and statistics majors (especially for prospective high school teachers, as many high schools are now teaching some of this material -- in fact it is required for secondary education math majors and minors). One student has commented that he wished he had taken APM 263 before taking MTH 275, since it helps with the notion of proof. A similar comment would presumably apply about taking this before MTH 302. The prerequisite for APM 263 reflects the needed mathematical maturity, not a reliance on specific facts or techniques from calculus. At least one section of the course is offered in each of fall and winter semesters, including at least one in the evening.]

APM 332 Applied Matrix Theory (4 credits)

Eigenvalues, eigenvectors and their applications, matrix calculus, linear differential equations, Jordan canonical forms, and quadratic forms. Time will also be spent on various computational techniques.
Prerequisite: MTH 275.
[This course, which very useful in applied mathematics of all kinds, is offered about once every two years.]

APM 357 Elements of Partial Differential Equations (4 credits)

Partial differential equations of physics, Fourier methods, Laplace transforms, orthogonal functions, initial and boundary value problems, and numerical methods.
Prerequisite: MTH 254 and APM 257 (or APM 255).
[This course is offered about once every two years.]

APM 367 Design & Analysis of Algorithm (4 credits)

Computer algorithms, their design and analysis. Strategies for constructing algorithmic solutions, including divide-and-conquer dynamic programming and greedy algorithms. Development of algorithms for parallel and distributed architectures. Computational complexity as it pertains to time and space is used to evaluate the algorithms. A general overview of complexity classes is given. Identical with CSE 361. Offered Fall and Winter, Prerquisites: CSE 231 and APM 263. [Algorithms are as much a part of mathematics as they are of computer science. This course is now cross-listed between the two departments and can be taught by faculty from either department.]

APM 381 Theory of Computation (4 credits)

Formal models of computation, including finite state automata, pushdown automata and Turing machines. Regular and context-free language. The computational models are used to discuss computability issues. Offered every Winter. Identical with CSE 343. Prerequisite: APM 367. [This is really much more a mathematics course than it is a computer science course. The course is now cross-listed between the two departments and can be taught by faculty from either department.]

APM 405 Special Topics (2 or 4 credits)

Advanced study of a selected topic in applied mathematics. May be repeated for additional credit.
Prerequisite: Permission of instructor.
[When a faculty member wishes to offer a course on a topic not otherwise represented in the catalog, this number is used. Interested students should talk to the faculty member teaching the course for all relevant information.]

APM 433 Numerical Methods (4 credits)

Propogation of errors, approximation and interpolation, numerical integration, methods for the solution of equations, Runge-Kutta and predictor-corrector methods. Offered fall of even-numbered years.
Prerequisite: MTH 275, APM 255 and knowledge of a scientific programming language, or permission of the instructor.
[This course uses a textbook such as Applied Numerical Methods for Engineers using MATLAB and C by Schilling and Harris. The course is usually taught simultaneously with APM 533, in the evening or late afternoon.]

APM 434 Applied Numerical Methods: Matrix Methods (4 credits)

Systems of linear equations, Gaussian elimination, LU factorization, approximation and curve fitting, eigenvalue problems, and nonlinear systems. Credit will not be granted for both APM 434 and CSE 418. Offered winter of odd-numbered years.
Prerequisite: MTH 254, MTH 275, and knowledge of a scientific programming language, or permission of the instructor.
[This course is independent of APM 433, but students can take both for a full-year study of numerical analysis. The course is usually taught simultaneously with APM 534.]

APM 455 Intermediate Ordinary Differential Equations (4 credits)

Review of elementary techniques, existence and uniqueness theory, series methods, systems of equations, oscillation and comparison theorems, Sturm-Liouville theory, stability theory and applications.
Prerequisite: APM 255 and MTH 452.
[This course is hardly ever offered.]

APM 463 Graph Theory and Combinatorial Mathematics (4 credits)

Introduction to combinatorics. Topics include techniques of enumeration, fundamental concepts of graph theory, applications to transport networks, matching theory and block designs. Offered every fall.
Prerequisite: MTH 275 and APM 263.
[This course has recently used the textbooks Graph Theory and Its Applications by Gross and Yellen and generatingfunctionology by Wilf; in the past it has often used Applied Combinatorics by Tucker or by Roberts. The course is usually taught simultaneously with APM 563, taken primarily by graduate students in the computer science masters degree program.]

APM 477 Computer Algebra (4 credits)

The mathematics and algorithms for symbolic computation. Includes theory of algebraic extensions, modular and p-adic methods, Groebner bases, factorization and zeros of polynomials, solutions to systems of polynomial equations, applications to automatic geometric theorem proving and closed form solutions to differential equations.
Prerequisite: MTH 275 and knowledge of a scientific computer programming language, or permission of instructor.
[This course is usually taught simultaneously with APM 577 and is offered about once every two years, in the evening. The current text is Modern Computer Algebra by von zur Gathen.]

APM 490 Independent Study (2 or 4 credits)

Reading or research on some topic in applied mathematics. May be repeated for additional credit.
Prerequisite: Permission of department.
[As the title indicates, a student takes this course on his/her own, rather than in a class. The subject matter can be anything that the student and the supervisor agree on, although usually independent study is not given in subjects regularly offered as courses. The format is also up to the participants, and can range from reading, oral reports, written reports, homework exercises to assisting a professor in a research project. Independent study at the freshman/sophomore level should be taken as MTH 290; for more advanced students, projects in pure mathematics should be given as MTH 490, projects in applied mathematics as APM 490, and projects in statistics as STA 490. Independent study is available during every term. Before registering for this course, of course, the student must make arrangements with a faculty member, and the two people involved should spell out what will be done, using a form supplied by the department.]

STA: STATISTICS

STA 225 Introduction to Statistical Concepts and Reasoning (4 credits)

Statistical ideas and thinking relevant to public policy, quality improvement, and physical and social sciences. Data collection and presentation; association; normal distribution; probability and simulation; and confidence intervals, p-values, and hypothesis testing. Satisfies the university general education requirement in mathematics, logic and computer science.
Prerequisite: MTH 012 or placement.
[This course currently uses the textbook The Basic Practice of Statistics by Moore. This is the less technical introduction to the subject, as compared to STA 226. STA 225 is appropriate for students in the social sciences and humanities, some sciences, elementary education, and nursing. Every educated citizen needs to know about statistics in order to understand what is happened in the world, whether it is about political polls, the risk of disease, games of chance, or any number of other topics. This is an excellent choice for fulfilling the general education requirement. Several sections, both day and evening, are offered fall and winter, and the course is usually offered in the spring and summer terms as well.]

STA 226 Applied Statistics (4 credits)

Introduction to statistics as applied to the physical, biological and social sciences and to engineering. Applications of special distributions and nonparametric techniques. Regression analysis and analysis of variance. Satisfies the university general education requirement in mathematics, logic and computer science.
Corequisite: MTH 122 or MTH 154.
[This course currently uses the textbook Statistics: Principes and Methods by Johnson; in the past it has also used Probability and Statistics for Engineers by Miller, Frend, and Johnson, and Statistics: The Exploration and Analysis of Data by Devore and Peck. It is the more rigorous introduction to the subject, as compared to STA 225, and it is appropriate for students in mathematics, statistics, the sciences, engineering, and computer science. This course is offered fall and winter semesters, during the day. Students who find it convenient to take this course in the evening may seek permission to take STA 501 (a course of about the same level of rigor and covering approximately the same topics) as a substitute.]

STA 322 Regression Analysis (4 credits)

Basic results from probability and statistics, linear regression, model testing and transformations, matrix methods in multiple regression, polynomial regression, indicator variables, stepwise and other search procedures. Offered every fall.
Prerequisite: STA 226 or permission of instructor.
[This course currently uses a textbook such as Applied Linear Regression Models by Neter, Kutner, Nachtsheim, and Wasserman, and is required of all statistics majors. It is offered every fall semester, in the evening, cross-listed with STA 502.]

STA 323 Design of Experiments (4 credits)

Planning of experiments, completely randomized, randomized block and Latin square designs, incomplete blocks, factorial and fractional factorial designs, confounding, and response surface methodology. Offered every winter.
Prerequisite: STA 226 or permission of instructor; STA 322 recommended.
[This course currently uses the textbook Statistical Principles of Research Design and Analysis by Kuehl and is virtually required of all statistics majors. It is offered every winter semester, in the evening, cross-listed with STA 503.]

STA 324 Analysis of Categorical Data (4 credits)

Analysis techniques for data obtained by counting responses in different categories. Discrete distributions, goodness of fit, contingency tables, association and agreement measures, loglinear and logit models.
Prerequisite: STA 322 or 323 or permission of instructor.
[This course is offered about once very two years, in the evening, cross-listed with STA 504.]

STA 405 Special Topics (2 or 4 credits)

Advanced study of a selected topic in statistics. May be repeated for additional credit.
Prerequisite: Permission of instructor.
[When a faculty member wishes to offer a course on a topic not otherwise represented in the catalog, this number is used. Interested students should talk to the faculty member teaching the course for all relevant information.]

STA 425 Elements of Stochastic Processes (4 credits)

Random walk models, Markov chains and processes, birth and death processes, queuing processes, diffusion processes and non-Markov processes.
Prerequisite: STA 427 or permission of instructor; APM 255 recommended.
[Do not be misled by the number--note that STA 427 is a prerequisite. The course is offered about once every two years, in the evening, cross-listed with STA 515.]

STA 426 Statistical Analysis by Graphical and Rank Order Methods (4 credits)

Exploratory data analysis, rank tests for location and scale, power of competing tests, confidence intervals, nonparametric analysis of variance methods.
Prerequisite: STA 427 or 322 or 323 or permission of instructor.
[Do not be misled by the number--note that STA 427 is a prerequisite. The course is offered about once every two years, in the evening, cross-listed with STA 526.]

STA 427 Introduction to Mathematical Statistics I (4 credits)

[catalog description for STA 427-428 together:] The distribution of random variables, conditional probability and stochastic independence, special distributions, functions of random variables, interval estimation, sufficient statistics and completeness, point estimation, tests of hypotheses and analysis of variance. Offered as fall-winter sequence every year.
Prerequisite: MTH 254, MTH 275, and STA 226 or permission of instructor.
[This course currently uses the textbook Introduction to Mathematical Statistics by Hogg. It is offered in the evening, simultaneously with STA 513.]

STA 428 Introduction to Mathematical Statistics II (4 credits)

[catalog description for STA 427-428 together:] The distribution of random variables, conditional probability and stochastic independence, special distributions, functions of random variables, interval estimation, sufficient statistics and completeness, point estimation, tests of hypotheses and analysis of variance. Offered as fall-winter sequence every year.
Prerequisite: STA 427.
[This is the continuation of STA 427; the course is really a year-long study of the mathematical foundations of the statistics. It is offered in the evening, simultaneously with STA 514.]

STA 490 Independent Study (2 or 4 credits)

Reading or research on some statistical topic. May be repeated for additional credit.
Prerequisite: Permission of department.
[As the title indicates, a student takes this course on his/her own, rather than in a class. The subject matter can be anything that the student and the supervisor agree on, although usually independent study is not given in subjects regularly offered as courses. The format is also up to the participants, and can range from reading, oral reports, written reports, homework exercises to assisting a professor in a research project. Independent study at the freshman/sophomore level should be taken as MTH 290; for more advanced students, projects in pure mathematics should be given as MTH 490, projects in applied mathematics as APM 490, and projects in statistics as STA 490. Independent study is available during every term. Before registering for this course, of course, the student must make arrangements with a faculty member, and the two people involved should spell out what will be done, using a form supplied by the department.]

MOR: OPERATIONS RESEARCH

MOR 242 Elementary Models in Operations Research (4 credits)

Basic techniques in deterministic modeling, Linear, combinatorial, and nonlinear models of real life applications are constructed, solved with optimization software and critically analyzed. Substantial writing component.
Prerequisite: MTH 155.
[This course is offered about once every two years and makes a good elective choice for mathematics and statistics majors interested in jobs in government or industry, as well as students from Engineering or Computer Science.]

MOR 454 Linear and Integer Optimization (4 credits)

Topics include linear and integer programming models, simplex method, complementary slackness, duality, sensitivity analysis, interior point methods systems of alternatives and branch-price-cut.
Prerequisite: MTH 254 and MTH 275.
[This course is offered about once every two years and makes a good elective choice for mathematics and statistics majors interested in jobs in government or industry.]

MOR 455 Nonlinear Optimization (4 credits)

Topics include nonlinear programming convex programming, unconstrained optimization, first and second order conditions, constrained optimization, KKT conditions, quadratic programming and separable convex programming.
Prerequisite: MOR 454.
[This course is offered about once every two years and makes a good elective choice for mathematics and statistics majors interested in jobs in government or industry.]

MOR 456 Stochastic Models in Operations Research (4 credits)

Stochastic processes including Markov chains with applications to the development and analysis of queuing models. Further topics drawn from such areas as reliability, decision analysis, stochastic inventory control and simulation.
Prerequisite: MTH 254 and MTH 275 and STA 226.
[This course is offered about once every two years and makes a good elective choice for mathematics and statistics majors interested in jobs in government or industry.]

MTE: MATHEMATICS FOR ELEMENTARY EDUCATION MAJORS

MTE 210 Numerical Structures (4 credits)

Elementary set and number theory. Components of the real number system. History of numeration. Algorithms of arithmetic. Other general algebraic structures. Problem solving. Enrollment limited to elementary education majors.
Prerequisite: MTH 012 or placement.
[This course currently uses the textbooks A Problem Solving Approach to Mathematics for Elementary School Teachers by Billstein et al., and Principles and Standards for School Mathematics from the NCTM. This is a content course, not a methods course, and mathematical projects are required in addition to tests, quizzes, and homework. The course is offered in the fall and winter semesters and is required of all elementary education majors. Click here for the course's home page for a recent offering.]

MTE 211 Structures of Geometry (4 credits)

An informal approach to geometry including topics from Euclidean and transformational geometries. Stress is placed on topics close to the elementary school curriculum such as mensuration formulae, ruler and compass construction, symmetries, congruence and similarity, and figures in two- and tree-dimensional Euclidean spaces. Enrollment is limited to elementary education majors.
Prerequisite: MTE 210.
[This course currently uses the textbook A Problem Solving Approach to Mathematics for Elementary School Teachers by Billstein et al. This is a content course, not a methods course, and several mathematical projects are often required in addition to tests, quizzes, and homework. The course is offered in the fall and winter semesters and is required of all elementary education majors who major or minor in mathematics. It is also highly recommended for all other elementary education majors. Click here for the course's home page for a recent offering.]

MTE 405 Special Topics (2 or 4 credits)

Study of mathematical topics particularly relevant for prospective teachers of elementary and middle school mathematics.
Prerequisite: MTE 211 or permission of instructor.
[Elementary education mathematics "majors" must take 30 credits of mathematical sciences courses. Since virtually all of our courses carry 4 credits, this creates a problem. Therefore this course, which will be offered every fall in the evening for 2 credits, allows these students to complete their requirements with a course specifically designed for them. It is also appropriate for minors who are a credit or two short because of transfer problems. Topics will vary by instructor. For the years 1999-2004 Professor Grossman's version of the course, as well as Professor Chipman's, has been a collection of interesting topics, partly based on Burger and Starbird's The Heart of Mathematics. For Fall 2005, Professor Grossman changed the focus entirely and taught a course based on some NCTM materials for middle school teachers. For Fall 2006, Professor Grossman is teaching a course revolving around middle school mathematics contests; click here for more information.]

MTE 410 Elementary School Mathematics and the Computer (4 credits)

An introduction to creative uses of computers in teaching mathematics in the elementary school, including program design, machine architecture, and the BASIC and LOGO computing languages. Enrollment is limited to elementary education majors.
Prerequisite: MTE 211, STA 225 and IST 396.
[This course is offered every winter semester, as well as spring and/or summer term, and is required of all elementary education mathematics majors and minors. Students who cannot fit this course into their schedules may substitute CSE 130, although they will not find that course geared to their needs as well as this one. Starting in Summer 2004 we are experimenting with adding Geometer's Sketchpad to the course.]

Return to Undergraduate Programs page.
Last updated: August 24, 2006. Send comments or corrections to Professor Grossman

Undergraduate Courses inthe Department of Mathematics and Statistics