# Courses

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 for subsequent courses.

Almost all courses are 4-credits, the main exceptions being 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 061 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.

Prerequisite: none.

[MTH 061 covers approximately the first half of the textbook

*Beginning and Intermediate Algebra*by Messersmith (while MTH 062 covers most of the second half), and it is offered every fall and winter (including an evening section in the fall), and usually also in the summer. The day sections are conducted in a lecture-workshop format; you need to sign up for the once-a-week lecture as well as the three-times-a-week workshops. 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 061; 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 061-062. 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 062 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.

Prerequisite: MTH 011 or placement.

[MTH 062 covers most of the second half of the textbook

*Beginning and Intermediate Algebra*by Messersmith (while MTH 061 covers approximately the first half), and it is offered in day and evening sections every fall and winter (and usually also in the summer). The day sections are conducted in a lecture-workshop format; you need to sign up for the once-a-week lecture as well as the three-times-a-week workshops. Students who have scored well on the mathematics portion of the ACT test (the current cut-off is 22 or higher) are considered to have placed out of MTH 062; 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 062 to determine whether they have the necessary background for it or whether they need to start in MTH 061. 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 061-062.]

**MTH 052 Intermediate Algebra Workshop (2 credits)**

[This course is no longer being 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 the formal reasoning knowledge foundation area.*

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 the formal reasoning knowledge foundation area.*

Prerequisite: MTH 062 or placement.

[This course currently uses the textbook

*Applied Mathematics for the Managerial, Life, and Social Sciences*by Tan. 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 062 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 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 the formal reasoning knowledge foundation area.*

Prerequisite: MTH 121 or MTH 141 or placement.

[This course currently uses the textbook

*Applied Mathematics for the Managerial, Life, and Social Sciences*by Tan. 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 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 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 062 or placement.

[This course currently uses the textbook

*Precalculus*by Barnett. 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 062. Algebra knowledge at the MTH 062 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. This course is offered in day and evening sections every fall and winter (and usually also in the summer). The day sections are conducted in a lecture-workshop format; you need to sign up for the three-times-a-week lecture as well as the two-or-three-times-a-week workshops.]

**MTH 142 Precalculus Workshop (2 credits)**

[This course is no longer being offered.]

**MTH 154 Calculus I (4 credits)**

A detailed study of limits, continuity, derivatives of algebraic and transcendental functions, applications of derivatives, numerical techniques, integrals and the Fundamental Theorem of Calculus.

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-84 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 the course is usually offered in the summer as well.]

**MTH 155 Calculus II (4 credits)**

A detailed study of methods of integration, applications of integrals, improper integrals, sequences, series and power series, polar coordinates, and parametric curves.

*Satisfies the university general education requirement for the knowledge application integration area. Prerequisite for knowledge applications: completion of the university general education requirement in the formal reasoning knowledge foundation area.*

Prerequisite: MTH 154.

[See the comments for MTH 154, of which this course is a continuation, using the same textbook. As with MTH 154, we are experimenting to improve students' success in this course. There are both day and evening sections fall and winter, and usually summer sections.]

**MTH 205 Special Topics (2 or 4 credits)**

Intermediate study of a selected topic in mathematics. May be repeated for additional credit.

[When a faculty member wishes to offer a sophomore-level 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 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, and the course is usually also offered in the summer.]

**MTH 256 Introduction to Linear Algebra (3 credits)**

[This course is no longer being offered.]

**MTH 266 Linear Algebra Laboratory (1 credit)**

[This course is no longer being offered.]

**MTH 275 Linear Algebra (4 credits)**

Study of general vector spaces, linear systems of equations, linear transformations and compositions, eigenvalues, eigenvectors, diagonalization, modeling and orthogonality. Provides a transition to formal mathematics. Replaces MTH 256. Student cannot receive credit for both MTH 256 and MTH 275.

Prerequisite: MTH 155.

[This course currently uses the textbook

*Elementary Linear Algebra*by Larson. The course is required of majors in mathematics, statistics, and computer science. 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 275 in fall and winter, and often one section in the summer.]

**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 semester. 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 301 Putnam Seminar (0 or 2 credits)**

This seminar meets one evening per week. Students solve and present solutions to challenging mathematical problems in preparation for the William Lowell Putnam Competition, a national undergraduate mathematics competition. May be repeated three times for additional credit.

Prerequisite: Permission of instructor.

[Oakland University usually enters a team in this competition, and this seminar is good preparation for the members of the team.]

**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 275 (or 256) or APM 263 permission of department.

[This course currently uses the textbook

*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 statements 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; some students have commented that taking APM 263 first is a good idea. MTH 302 is offered in the fall and winter semesters usually in the late afternoon.]

**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 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 an advanced 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 302. Satisfies the university general education requirement for a writing intensive course in the major. Prerequisite for writing intensive: completion of the university writing foundation requirement.

[This 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 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 also complete the sequel, MTH 453.]

**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 452.

[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 only occasionally 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 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 textbooks such as

*Euclidean and Non-Euclidean Geometry*by Greenberg or

*The Four Pillars of Geometry*by Stillwell. Click here for the website for the course in Fall 1998. The course that semester 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 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 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 302.

[This course often 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) who want an additional elective, as well as for computer science majors. Both the theoretical aspects of the subject and modern applications, such as to cryptography, as studied, and sometimes computer assignments are a major part of the course.]

**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)**

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 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 or MTH 154.

[This course currently uses the textbook

*Discrete Mathematics*by Ensley. It is required of students in the Information Technology program and is usually offered fall and winter.]

**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 summer 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-84 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)**

[This course is no longer being offered, but students who take a differential equations course at another school often get transfer credit for this course. It can be used in place of APM 255 as a mathematics elective for math, stat, or actuarial science majors. Engineering students can complete a requirement of APM 255 for their engineering major by taking MTH 275 in addition to APM 257.]

**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). Some students have commented that they wished they had taken APM 263 before taking MTH 275 or MTH 302, since it helps with the notion of proof. The prerequisite for APM 263 reflects the needed mathematical maturity, not a reliance on specific facts or techniques from calculus. Click here for the website for the course in Winter 2010. 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 255 (or APM 257).

[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.

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. 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. Click here for the website for the course in Winter 2009. It is usually offered in the winter semester.]

**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 text might be

*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 the formal reasoning knowledge foundation area.

Prerequisite: MTH 062 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 Probability and 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 the formal reasoning knowledge foundation area.

Pre- or corequisite: MTH 122 or MTH 154.

[This course currently uses the textbook

*Probability and Statistics for Engineering and Science*by Devore. 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 227 Introduction to Statistical Methods (4 credits)**

Introduction to statistical thinking and applications to industrial and similar processes. Descriptive statistics, distributions, and probability models useful in process control and systems reliability; confidence intervals, hypothesis testing, regression, and basic experimental design. Statistical concepts to be reinforced with case studies promoting problem solving skills and statistical thinking. STA 227 cannot be used to replace STA 226.

Prerequisite: MTH 121 or MTH 141.

[This course is designed for majors in Information Technology. The current textbook is

*Basic Engineering Data Collection and Analysis*by Vardeman.]

**STA 228 Statistical Methods for Biology (4 credits)**

Introduction to statistical methods for students in biology and other laboratory sciences. Basic principles of experimental design and data collection. Descriptive statistics, probability models, confidence intervals, hypothesis testing, two- and multi-sample comparisons, regression models, categorical data, nonparametric methods. Mathematics or statistics majors cannot use STA 228 to replace STA 226.

Prerequisite: MTH 141.

[This course is designed for majors in the biological sciences. The current textbook is

*The Basic Practice of Statistics in the Life Sciences*by Baldi.]

**STA 402 Applied Linear Models I (4 credits)**

Basic results from probability and statistics, linear regression, model testing and transformations, matrix methods in multiple regression, polynomial regression, indicator variables, basics of experimental design, one-way ANOVA with fixed and random effects.

Prerequisite: STA 226 or permission of instructor.

[This course currently uses the textbook

*Applied Linear Statistical Models*by Kutner, and is required of all statistics majors. It is offered every fall semester, in the evening, cross-listed with STA 502.]

**STA 403**

**Applied Linear Models II (4 credits)**

Multiway ANOVA, randomized block and Latin square designs, incomplete blocks, factorial and fractional factorial designs, confounding, response surface methods, random and mixed models, introduction to generalized linear models.

Prerequisite: STA 226 or permission of instructor; STA 322 recommended.

[This is a continuation of STA 402; all statistics majors should take it. It is offered every winter semester, in the evening, cross-listed with STA 503.]

**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 424 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 402 or permission of instructor.

[This course is offered about once very two years, in the evening, cross-listed with STA 504.]

**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 Nonparametric Methods (4 credits)**

Permutation and rank tests for location and scale, bootstrapping, power of competing tests, confidence intervals, nonparametric regression and analysis of variance methods, density estimation.

Prerequisite: STA 402 or 427 or permission of instructor.

[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)**

The distribution of random variables, conditional probability and stochastic independence, special distributions, functions of random variables.

Prerequisite: MTH 254, MTH 275, and STA 226 or permission of instructor.

[This course uses a textbook such as

*Introduction to Mathematical Statistics*by Hogg. It is offered in the evening every fall, simultaneously with STA 513.]

**STA 428 Introduction to Mathematical Statistics II (4 credits)**

Interval estimation, sufficient statistics and completeness, point estimation, tests of hypotheses and analysis of variance.

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 every winter, 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 062 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 from 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 from 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. May be repeated for additional credit.

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, was been a collection of interesting topics, partly based on Burger and Starbird's

*The Heart of Mathematics*. In Fall 2005, Professor Grossman changed the focus entirely and taught a course based on some NCTM materials for middle school teachers. In Fall 2006 and Fall 2008, Professor Grossman taught a course revolving around middle school mathematics contests; click here for more information. In Fall 2007 Professor Kruk and his students delved into various aspects of the concept of number.]

**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 in the summers, 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. We also sometimes include

*The Geometer's Sketchpad*in the course.]

Last updated: November 1, 2013. Send additions or corrections (or other comments) to Professor Grossman.