MU Department of Mathematics, Statistics and Computer Science

Mathematics Handbook for 2007-2008

Updated November 27, 2007

INTRODUCTION

Before entering Marquette University, most students' mathematical experience has been with applications in which mathematics is seen primarily as a problem-solving tool. Courses in algebra, geometry and perhaps calculus usually stress this aspect of mathematics. These courses concentrate on the skills of formulating a problem in precise terms and then solving it by applying a series of manipulations or formulas, some of which are thousands of years old. There is however, another aspect of mathematics which beginning students rarely glimpse - so-called pure mathematics. This is the creative side of mathematics in which new systems and formulas are discovered or derived. Here lies the challenge to reach beyond the world as we know it and to speculate, to invent.

In reality, the categories of pure and applied mathematics are not as distinct as they may first appear. Today's applied problem often leads to tomorrow's theory. And, just as often, what was yesterday's esoteric theory provides the practical solution to today's technical challenges. So, for example, modern computer circuitry was developed using the tools of mathematical logic invented in the late 1800's. And the mathematical limitations of computing machinery were derived decades before the physical machines existed. Likewise, the practical problem of errors in transmitting information over telephone lines or satellite channels led to a whole new field of mathematical investigation - "error-correcting codes."

Because of this continuing interplay between pure theory and practical applications, the mathematics curriculum at Marquette University is designed to open the door to the creative side of mathematics while also providing an atmosphere in which each student's application skills can continue to grow. The curriculum can be tailored to fit an individual's interest. Some students choose to concentrate on subjects with immediate applications such as probability, statistics and differential equations. Others choose to pursue more abstract topics such as modern algebra, topology or logic. Others are interested in preparing to teach mathematics at the primary or secondary level. In any case the curriculum is designed to provide the technical skills for growth in the discipline.

ADVISING and PRE-REGISTRATION

A student planning to complete a major in mathematics should enroll in MATH 080 in the first semester of his or her freshman year and in MATH 081 in the second semester. As soon as he or she has decided to major in the Department, the student should report to the Department office (room 340 of Cudahy Hall) to declare a major and to be assigned a departmental advisor. From this time on, the student meets with his advisor to discuss course selections for the next semester and general academic progress, as well as to receive access to pre-registration through the TVR system.

REQUIREMENTS FOR THE MATHEMATICS MAJOR

All students must take the following five mathematics courses:

MATH 080	Calculus 1	4 sem. hrs.
MATH 081	Calculus 2	4 sem. hrs.
MATH 082	Calculus 3	4 sem. hrs.
MATH 091	Foundations of Mathematics	3 sem. hrs.
MATH 121	Linear Algebra	3 sem. hrs.

In addition, all students must take at least one computer science course offered by the Department. Normally, this will be either COSC 050, Introduction to Computer Science or COSC 060, Object-Oriented Programming, but other courses may be substituted depending on the student's background in computer science.

ELECTIVES

To complete a major, twenty-one additional hours of upper division MATH courses are required. These must include at least three of the following:

MATH 112	Topology	3 sem. hrs.
MATH 124	Abstract Algebra 1	3 sem. hrs.
MATH 135	Foundations of Geometry	3 sem. hrs.
MATH 140	Theory of Differential Equations	3 sem. hrs.
MATH 160	Theory of Probability	3 sem. hrs.
MATH 180	Intermediate Analysis 1	3 sem. hrs.

The remaining electives may be selected from any of the courses listed above or any other upper division MATH courses offered by the Department.

COURSE SELECTION

A mathematics major must complete the requirements for the major listed on the previous page and must also satisfy the graduation requirements of the College of Arts and Sciences as described in the University Undergraduate Bulletin. A suggested curriculum for mathematics majors can be found in the Bulletin under Curricula Information, Arts and Sciences and in this handbook. Both the requirements for the major and the general graduation requirements are flexible enough to allow each student to select a variety of courses. The following groupings of courses are intended to aid students in making these selections.

Pure Mathematics (with an emphasis on preparing for advanced study)

MATH 112 Topology
MATH 124 Abstract Algebra 1
MATH 140 Theory of Differential Equations
MATH 160 Theory of Probability
MATH 180 Intermediate Analysis 1
MATH 182 Complex Variables
(MATH 125 and 181 are also strongly recommended)

Statistics and Actuarial Science

MATH 124 Abstract Algebra 1
MATH 146 Numerical Analysis
MATH 160 Theory of Probability
MATH 161 Mathematical Statistics
MATH 162 Time Series Analysis
MATH 163 Regression Analysis
MATH 167 Theory of Optimization
MATH 168 Computational Statistics
MATH 180 Intermediate Analysis 1

Applied Mathematics

MATH 124 Abstract Algebra 1
MATH 140 Theory of Differential Equations
MATH 142 Elementary Partial Differential Equations
MATH 146 Numerical Analysis
MATH 147 System Modeling Analysis
MATH 162 Time Series Analysis
MATH 163 Regression Analysis
MATH 166 Biomathematics
MATH 167 Theory of Optimization
MATH 180 Intermediate Analysis 1
MATH 182 Complex Variables

Teaching Secondary Mathematics

MATH 124 Abstract Algebra 1
MATH 135 Foundations of Geometry
MATH 138 Topics in Elementary Mathematics from an Advanced Standpoint
MATH 164 Statistical Methods
MATH 137 The Teaching of Mathematics
EDUC 130 Student Teaching

COMBINED MAJORS AND MINORS

Major in MATHEMATICS and COMPUTER SCIENCE:

A student with a major in mathematics will need to complete the requirements for the computer science major, which are: thirty-three hours of COSC courses, including: COSC 060, 061, 065, 066, 125, 126, 152 and fifteen additional hours of upper division COSC courses. One of these courses will be used to satisfy the COSC requirement for the major in mathematics. MATH 080 will substitute for the MATH 071 requirement of the COSC major, and MATH 147 is required as a MATH elective.

Major in MATHEMATICS and MINOR in COMPUTER SCIENCE:

A student with a major in mathematics will need to complete the computer science requirements for the computer science minor, which are: COSC 060, 061, 065, 066, and six additional hours of upper division COSC courses. One of these may be used to satisfy the COSC requirement for the major in mathematics.

Major in MATHEMATICS and MINOR in SOFTWARE DEVELOPMENT:

A student with a major in mathematics needs to complete the computer science requirements for the software development minor, which are: COSC 060, 061, 065, 162, and six additional hours of upper division COSC courses. One of these may be used to satisfy the COSC requirement for the major in mathematics.

Major in MATHEMATICS and MINOR in SECONDARY EDUCATION:

A student intending to obtain a certificate to teach secondary mathematics is urged to see the Department Advisor for secondary teaching majors before the start of classes in the first semester of his or her FRESHMAN year! In order to complete the required major in mathematics and a minor in education in a four year program, students must follow a very precise schedule. There is a complex set of prerequisites and some courses are offered only once every two years.

Major in MATHEMATICS and MINOR in BUSINESS ADMINISTRATION:

A student with a major in mathematics will need to complete the requirements for the Minor in Business Administration as described in the College of Business Administraton section of the Undergraduate Bulletin. Although these total thirty semester hours, there is some overlap with requirements of the College of Arts and Sciences. See the sample curriculum in the following pages.

BACHELOR OF SCIENCE (FOR MATHEMATICS MAJORS)

Students planning to complete a teaching major in mathematics should consult the outlines later in this section.

F r e s h m a n

First Term	Sem. Hr.(16-17)
ENGL 001	3
Foreign Language	3-4
HIST 001 or 002	3
MATH 080	4
Social-Behavioral Science	3

Second Term	Sem. Hr.(16-17)
ENGL 002	3
Foreign Language	3-4
History or Social-Behavioral Science	3
MATH 081	4
Elective	3

S o p h o m o r e

First Term	Sem. Hr.(17)
MATH 082	4
MATH 091	3
Literature	3
Natural Science	4
Elective	3

Second Term	Sem. Hr.(16)
MATH 121	3
Literature	3
Natural Science	4
PHIL 050	3
Elective	3

J u n i o r

First Term	Sem. Hr.(16)
MATH Sequence (Part 1)	3
MATH Group 1 (Pure)	3
COSC 060	4
THEO 001	3
Electives	3

Second Term	Sem. Hr.(15-18)
MATH Sequence (Part 2)	3
MATH Group 3 (Statistics)	3
PHIL 104	3
Electives	6-9

S e n i o r

First Term	Sem. Hr.(15-18)
MATH Group 2 (Applied)	3
MATH elective	3
Philosophy (upper division)	3
Theology (second level)	3
Electives	3-6

Second Term	Sem. Hr.(15-18)
MATH elective	3
Theology (third level)	3
Diverse Cultures electives	3
Electives	6-9

Taking the minimum number of hours each term will not accumulate sufficient hours for graduation in four years.
MATH 082 and MATH 090 can be taken in either order or concurrently.
Potential mathematics majors who have taken a university-level calculus course in high school should discuss with the department the possibility of credit by examination for MATH 080 and/or 081 or placement in MATH 081 or 082 before registering for a calculus course.

SAMPLE CURRICULUM For Mathematics Major with a Business Administration Minor*

F r e s h m a n

First Term	Sem. Hr.(16-17)
ENGL 001	3
Foreign Language	3-4
HIST 001 or 002	3
MATH 080	4
ECON 043	3

Second Term	Sem. Hr.(16-17)
ENGL 002	3
Foreign Language	3-4
History or Social-Behavioral Science	3
MATH 081	4
ECON 044	3

S o p h o m o r e

First Term	Sem. Hr.(16)
MATH 091	4
Literature	3
ACCO 030	3
THEO 001	3
Elective	3

Second Term	Sem. Hr.(15)
Literature	3
MATH 082	3
ACCO 031	3
PHIL 050	3
Elective	3

J u n i o r

First Term	Sem. Hr.(16-19)
MATH 164	3
MATH 121	3
Natural Science	4
Electives	6-9

Second Term	Sem. Hr.(16-19)
Math electives	6-9
Computer Science elective	3
Natural Science	4
PHIL 104	3

S e n i o r

First Term	Sem. Hr.(18)
Math electives	6
Philosophy (upper division)	3
FINA 180	3
MARK 140	3
Theology (second level)	3

Second Term	Sem. Hr.(16-18)
Math electives	6
Business elective	3
MANA 156	3
Theology (third level)	3
Diverse Cultures elective	3

Taking the minimum number of hours each semester will not accumulate sufficient hours for graduation in four years.
MATH 082 and MATH 091 can be taken in either order or concurrently.
Potential mathematics majors who have taken a university level calculus course in high school should discuss with the Department the possibility of credit by examination for MATH 080 and/or 081 or placement in MATH 081 or 082 before registering for a calculus course.

STUDENT COMPUTING FACILITIES

Katherine Reed Cudahy Hall houses the University's central computing facility, maintained by Information Technology Services (ITS) in room 108, as well as the MSCS Department's computing facilities on the first, third, or fourth floors.

Each student enrolled at Marquette is granted an account on the Emarq/CheckMarq systems maintained by ITS. Accounts on the Emarq are obtained by applying in Room CU 293 and are maintained throughout the student's enrollment at Marquette. Additional information regarding University computing facilities can be obtained by calling ITS Help Desk at 288-7799.

Students enrolled in MSCS courses or registered as majors are also given access to the MSCS computing facilities (CU 101; 301 or 310; 410 or 412) available within the department. The MSCS computing facility consists of a network of SUN computers running the UNIX operating system, and PCs running Windows and Linux. Access to the MSCS computers is available directly through the first, third, and fourth floor laboratories of Cudahy Hall. The department also provides computing resources specifically to particular undergraduate and graduate courses (e.g., networks, hardware) and faculty research.

Although students may have their own computing equipment, the resources provided by the department are all that are required for course work. Students are encouraged to use the department's facilities since it is through these efforts that they learn the ins and outs of the UNIX/Linux/Windows operating systems, gain access to the Internet, and conveniently submit homework assignments.

Last updated date: 02/20/2007