2004-06 IUPUI Campus Bulletin

Department of Mathematical Sciences

Professors Abramovich, Bittinger, Bleher, Boukai (Chairperson), Burkinshaw, Frankel, A. Its, Kaminker, Kleyle, Kuczkowski, Misiurewicz, Ng, Penna, Sen, Wojciechowski Professors Emeriti Alton, Crown, Hutton, Rothman Associate Professors Geller, Ji, Klimek, Luke, Miller (IUPU Columbus), Patterson, Podgorski, Rigdon (Associate Chairperson), Sarkar, Shen, Tam, Wang, Watt (Associate Chairperson) Assistant Professors Ernst, Mukhin Adjunct Professors Aliprantis, Reid Lecturers Cooley, E. Its, Rangazas, Ziemian Mathematical sciences include the areas of pure and applied mathematics, mathematics education, and statistics. Mathematics involves the study of problems in areas such as algebra, geometry, analysis, and logic, and of problems arising in the real world. Mathematics and statistics are used in the physical sciences, engineering, and the social, life, and management sciences. Mathematics education involves the training of prospective secondary teachers.

Degree Programs

The department offers the Purdue University Bachelor of Science degree in mathematics with options in pure mathematics, applied mathematics, actuarial science, and secondary school teaching.

Purdue graduate degrees offered include the Master of Science, Master of Science (Option for Teachers), Master of Science (Concentration in Applied Statistics), and Master of Science (Concentration in Industrial and Applied Mathematics). Additionally, qualified students may be authorized to pursue the Ph.D. in mathematics in areas where a program has been arranged with Purdue, West Lafayette.

Bachelor of Science

Students are encouraged to declare a mathematics major in the freshman year so they can receive proper academic advising. A grade point average of 2.5 with no failing grades in mathematics courses through MATH 351 is a minimum indication of success in this major.

Degree Requirements

The baccalaureate degree general requirements, the area requirements, and the Bachelor of Science degree requirements are listed earlier in this bulletin (see the School of Science requirements under ''Undergraduate Programs''). For a Bachelor of Science degree in mathematics, the following additional requirements and restrictions apply: Area I No additional requirements. The second semester of English composition may be satisfied by ENG W132 (or ENG W150), ENG W231, or TCM 320. Area II All degree options require 5 credit hours in a modern foreign language. Area III The following apply to all degree options:

1. Mathematics courses below MATH 163 and those mathematics courses in which the student has received grades below C- do not count toward the degree.
2. Certain courses, such as CHEM C101, C102, C110; PHYS 100, 200, 218, 219, P201, P202; and AST A100 and A105 may not be used to fulfill the science requirement, Area IIIC, of the School of Science. If in doubt about a particular course, the student should consult a mathematics department advisor.
3. The Area IIID computer science requirement must be in a higher-level programming course (not BASIC). A grade of C (2.0) or better is required.

Area IV Mathematics courses in which a student has received grades below C (2.0) do not count in area IV. The Area IV requirements for the secondary area of concentration and the major for the four degree options-pure mathematics, applied mathematics, actuarial science, and secondary teaching-are described in the following sections. There is no single semester-by-semester plan of study for any of the options because flexibility is encouraged within the various programs. However, a sample program that shows one possible sequence of courses is given for each option. Variations from the sample program should be made in consultation with the student's advisor. Because of the complexity of the requirements, and because certain courses are not offered every semester, it is important that each student consult the assigned advisor as soon as possible in order to proceed through a proper plan of study for the chosen degree program. A minimum grade point average of 2.5 is required in all mathematics courses that count toward the major. Area IV Secondary Area of Concentration Requirements So that each student can acquire some depth of study in a subject outside of the major area, the Department of Mathematical Sciences requires students to have a secondary area of concentration outside of the department. The secondary area of concentration consists of at least 18 credit hours and includes at least three courses beyond the introductory level. It is subject to the approval of the student's advisor. Although a secondary area of concentration is usually in one department, it may be from two or more if the advisor approves.

Courses may be used for the double purpose of fulfilling the general requirements and also for fulfilling the secondary area of concentration requirements of the Department of Mathematical Sciences. For students in the Pure Mathematics Option or the Applied Mathematics Option, a secondary area in one of the physical sciences or in a subject that makes serious use of mathematics, such as computer science, engineering, or economics, is desirable. Students in the Secondary School Teaching Option satisfy the requirements for a secondary area by the courses they take to meet the professional education requirement.

The requirement of 18 credit hours in a secondary area of concentration does not, by itself, constitute an official minor that would be acknowledged on the student's transcript. A minor must be offered through the department or school in which the minor is taken. One such minor, which is designed to be of particular interest to students choosing a career in actuarial sciences, is offered by the School of Business in conjunction with the Department of Mathematical Sciences. Students interested in the business minor for mathematics majors should contact the Department of Mathematical Sciences or the School of Business for exact requirements.

Area IV Major Requirements

PURE MATHEMATICS OPTION

With this option, students will be well prepared for graduate work in pure mathematics. However, students with undergraduate degrees in pure mathematics have also been successful with graduate studies in business administration, computer science, economics, engineering, educational research, law, medicine, operations research, psychology, statistics, and physics. Persons with advanced degrees in pure mathematics find careers primarily in college teaching, but careers in business, industry, or government service are also possible.

The Area IV major requirements are as follows:

1. Core curriculum: MATH 163, 164, 261, 262, and 351.
2. Analysis: MATH 441-442.
3. MATH 453 Beginning Abstract Algebra.
4. MATH 462 Elementary Differential Geometry or MATH 510 Vector Calculus.
5. 12 additional credit hours in mathematics or statistics courses at the 300 level or higher. Courses in computer science or courses in other departments of the School of Science that have an appropriate mathematical content may be selected with the approval of the advisor. Normally, no more than 6 credit hours will be approved outside of mathematics and statistics.
6. The 45 credit hours of courses required above must include at least 6 credit hours from a course sequence listed below, other than MATH 441-442.
7. 1-3 hours of MATH 490 or MATH 492 Capstone Experience.

Course Sequences

Advanced calculus	MATH 510 and 525
Algebra	MATH 453, and 505 or a higher-level algebra course
Analysis	MATH 441, and 442 or a higher-level analysis course
Geometry	MATH 462, and 561 or a higher-level geometry course
Differential equations	MATH 520, and 537 or higher-level differential equations course
Modeling	MATH 426, and 417 or a higher-level modeling course
Numerical analysis	MATH 414, and CSCI 515 or a higher-level numerical analysis course
Probability and Statistics	Two STAT courses numbered 311 or higher
Scientific computing	CSCI 475 and 476
Theoretical computer science	CSCI 340 and 470

Pure Mathematics Option Sample Program (124 cr. required)

Freshman Year
First Semester
	MATH 163	Integrated Calculus and Analytic Geometry I	5
	COMM R110	Fundamentals of Speech Communication	3
	ENG W131	Elementary Composition I	3
	SCI 120	Windows on Science	1
	Physical or Biological Science with Laboratory		5
17
Second Semester
	MATH 164	Integrated Calculus and Analytic Geometry II	5
	CSCI 230	Computing I	4
	Second Composition Course		3
	Physical or Biological Science		3
15
Sophomore Year
Third Semester
	MATH 261	Multivariate Calculus	4
	HIST H114	History of Western Civilization II	3
	Physical or Biological Science		3
	Free Electives		6
16
Fourth Semester
	MATH 262	Linear Algebra and Differential Equations	4
	MATH 351	Elementary Linear Algebra	3
	Humanities-List H		3
	Physical or Biological Science		3
	Free Elective		3
16
Junior Year
Fifth Semester
	MATH 441	Foundations of Analysis	3
	MATH or STAT	Elective	3
	Foreign Language		5
	Social Sciences-List S		3
	Free Elective		3
17
Sixth Semester
	MATH 442	Foundations of Analysis II	3
	MATH 510	Vector Calculus	3
	Comparative World Cultures-List C		3
	Free Electives		6
15
Senior Year
Seventh Semester
MATH 453		Beginning Abstract Algebra	3
	MATH or STAT	Elective	3
	Junior/Senior Integrator		3
	Free Electives		6
15
Eighth Semester
	MATH or STAT	Electives	6
	MATH 492	Capstone Experience	2
	Free Electives		6
	CAND 991	Candidate for Graduation	0
14

APPLIED MATHEMATICS OPTION

Graduates with training in applied mathematics are employed in business, industry, and government. They would probably work as part of a team and would often need to communicate mathematical ideas to persons trained in other subjects. In many instances, they would need to formulate problems for solution on a computer and then interpret the answers. Thus, besides a fundamental knowledge of mathematics, a knowledge of what computers can do is essential. This option is also a good preparation for graduate study in applied mathematics, computer science, statistics, and engineering.

The Area IV major requirements are as follows:

1. Core curriculum: MATH 163, 164, 261, 262, and 351.
2. MATH 414 Numerical Methods.
3. MATH 510 Vector Calculus.
4. Mathematical modeling: MATH 417 or 426.
5. 15 additional credit hours in mathematics or statistics courses at the 300 level or higher. Courses in computer science or courses in other departments of the School of Science that have an appropriate mathematical content may be selected with the approval of the advisor. Normally, no more than 6 credit hours will be approved outside of mathematics and statistics.
6. The 45 credit hours of courses required above must include at least 6 credit hours in each of two of the course sequences listed below. Students planning on attending graduate school in mathematics are advised to take MATH 441-442.
7. 1-3 credit hours of MATH 490 or MATH 492 Capstone Experience.

Course Sequences

Advanced calculus	MATH 510 and 525
Algebra	MATH 453, and 505 or a higher-level algebra course
Analysis	MATH 441, and 442 or a higher-level analysis course
Differential equations	MATH 520, and 537 or a higher-level differential equations course
Geometry	MATH 462, and 561 or a higher-level geometry course
Modeling	MATH 426, and 417 or a higher-level modeling course
Numerical analysis	MATH 414, and CSCI 515 or a higher-level numerical analysis course
Probability and Statistics	Two STAT courses numbered 311 or higher
Scientific computing	CSCI 475 and 4761
Theoretical computer science	CSCI 340 and 4701

1 Students are generally allowed to select only one of these two course sequences.

Applied Mathematics Option Sample Program (124 cr. required)

Freshman Year
First Semester
	MATH 163	Integrated Calculus and Analytic Geometry I	5
	ENG W131	Elementary Composition I	3
	SCI 120	Windows on Science	1
	CSCI 230	Computing I	4
	HIST H114	History of Western Civilization II	3
16
Second Semester
	MATH 164	Integrated Calculus and Analytic Geometry II	5
	COMM R110	Fundamentals of Speech Communication	3
	Second Composition Course		3
	Free Electives		6
17
Sophomore Year
Third Semester
	MATH 261	Multivariate Calculus	4
	PHYS 152	Mechanics	4
	Humanities-List H		3
	Free Electives		6
17
Fourth Semester
	MATH 262	Linear Algebra andDifferential Equations	4
	MATH 351	Elementary Linear Algebra	3
	PHYS 251	Heat, Electricity, and Optics	5
	Free Elective		3
15
Junior Year
Fifth Semester
	MATH 414	Numerical Methods	3
	PHYS 310	Intermediate Mechanics	4
	MATH or STAT	Elective	3
	Foreign Language		3
	Social Sciences-List S		3
16
Sixth Semester
	MATH 426 or MATH 417	Introduction to Applied Mathematics and Modeling Discrete Modeling and Game Theory	3
	MATH 510	Vector Calculus	3
	PHYS 342	Modern Physics	3
	Comparative World Cultures-List C		3
	Foreign Language		3
15
Senior Year
Seventh Semester
	MATH or STAT Electives		6
	Junior/Senior Integrator		3
	Free Electives		6
15
Eighth Semester
	MATH or STAT Electives		6
	MATH 492	Capstone Experience	2
	Free Electives		6
	CAND 991	Candidate for Graduation	0
14

ACTUARIAL SCIENCE OPTION

The goal of this option is to prepare students to take the first two and possibly the third actuarial exams by the end of their senior year. In addition to the core curriculum, this option requires a one-year sequence in probability and mathematical statistics, another one-year sequence in actuarial models, and a course on the mathematical theory of interest. In addition, a minor in business and economics will be required to help prepare for the second exam. (This minor will serve as the secondary area of concentration.) As this bulletin goes to print, further details are not available. Contact the Department of Mathematical Sciences for an updated plan of study.

SECONDARY SCHOOL TEACHING OPTION

Students who wish to teach in secondary schools must meet the requirements for teacher certification in the state in which they expect to teach. Interested persons can obtain these requirements by writing to the Department of Public Instruction, Certification Office, in the capital city of any state.

In order to satisfy Indiana state law, a student should have 40 credit hours in general education courses and a specified core of professional education courses as part of the requirement for a teaching license. Students should be sure to see an advisor to ensure that these hours are properly distributed and that the professional education requirements are met. The IUPUI secondary teaching program that has been approved by the state of Indiana requires the completion of at least 36 credit hours of mathematics courses.

The Area IV major requirements are as follows:

1. Core curriculum: MATH 163, 164, 261, 262, and 351.
2. MATH 300 Logic and the Foundations of Algebra.
3. MATH 453 Abstract Algebra.
4. MATH 463 Intermediate Euclidean Geometry for Secondary Teachers.
5. Probability and statistics: STAT 311 or 350 or 416 or 511.
6. MATH 583 History of Elementary Mathematics.

Secondary School Teaching Option Sample Program (124 cr. required)

Freshman Year
First Semester
	MATH 163	Integrated Calculus and Analytic Geometry I	5
	ENG W131	Elementary Composition I	3
	PSY B104	Psychology as a Social Science	3
	HIST H114	History of Western Civilization II	3
	SCI 120	Windows on Science	1
15
Second Semester
	MATH 164	Integrated Calculus and Analytic Geometry II	5
	COMM R110	Fundamentals of Speech Communication	3
	ENG W132	Elementary Composition II	3
	Humanities-List H		3
14
Sophomore Year
Third Semester
	MATH 261	Multivariant Calculus	4
	MATH 300	Logic and the Foundations of Algebra	3
	CSCI 230	Computing I	4
	Physical or Biological Science with Laboratory		4
15
Fourth Semester
	MATH 262	Linear Algebra and Differential Equations	4
	Physical or Biological Science		3
	EDUC M300 and EDUC K205 and EDUC M201	Teaching in a Pluralistic Society Intro to Special Education Field Experience	3 3 0
	EDUC P255 and EDUC M201	Educational Psychology Field Experience	3 1
17
Junior Year
Fifth Semester
	MATH 351	Elementary Linear Algebra	3
	Physical or Biological Science		3
	Foreign Language		5
	MATH 424 and Math 425 (or EDUC M457)	Teaching of Math in Middle School and Junior High School Teaching Math in Secondary School	5
16
Sixth Semester
	STAT 511	Statistical Methods	3
	EDUC M464	Methods of Teaching Reading	3
	Physical or Biological Science		3
	MATH 463	Intermediate EuclideanGeometry for Secondary Teachers	3
	Junior/Senior Integrator		3
15
Senior Year
Seventh Semester
	MATH 453	Abstract Algebra	3
	EDUC H340	Education and American Culture	3
	EDUC M314 and EDUC M301	General Methods for SeniorHigh/Junior High/Middle School Teachers Field Experience	3
	Comparative World Cultures-List C		3
	Free Elective		3
15
Eighth Semester
	EDUC M470	Practicum	6
	EDUC M480	Student Teaching: Secondary	10
	MATH 583	History of Mathematics	3
	CAND 991	Candidate for Graduation	0
19

Minor in the Mathematical Sciences

An undergraduate minor in mathematics would be useful in many fields. A scientist or engineer may need a knowledge of differential equations and linear algebra, while someone in business or a social science may need a background in probability or statistics.

Requirements

1. The calculus sequence MATH 163, 164, and 261 (14 cr.).
2. Two additional courses selected from mathematics courses numbered 262 or higher or from statistics courses numbered 311 or higher.
3. 9 credit hours of the minor must be completed at IUPUI.
4. The grade in each course submitted for the minor must be C (2.0) or higher.

Correspondence courses may not be used to fulfill requirements for the minor.

Graduate Programs

The Department of Mathematical Sciences offers graduate training leading to the Purdue University Master of Science degree. Qualified students may be authorized to pursue the Ph.D. in mathematics at IUPUI in areas where a program has been arranged with Purdue, West Lafayette. The M.S. degree requires two years of graduate study, and the Ph.D. degree typically requires two to three additional years of study.

Admission Requirements

Students entering a graduate program in mathematics should have completed an undergraduate program containing as many courses as possible in abstract algebra, linear algebra, advanced calculus, differential equations, logic and foundations, and probability.

Students entering the graduate program in applied mathematics or the graduate program in industrial and applied mathematics should have completed an undergraduate program in mathematics or an undergraduate program in engineering or physical sciences that was strongly oriented toward mathematics.

Students entering the master's program in applied statistics must have a bachelor's degree from an accredited institution. The minimal mathematics requirement for admission to this program includes an undergraduate sequence in univariate and multivariate calculus (equivalent to MATH 163, 164, 261) and one mathematics course beyond the calculus level. Prospective applicants who do not have this background must take all or part of the calculus sequence prior to admission to the program. Applicants who lack a course beyond the calculus sequence must complete such a course as soon as possible after conditional admission.

Application for Admission

Students who wish to pursue an advanced degree in the Department of Mathematical Sciences should fill out a graduate student application form. Applicants are encouraged to submit GRE scores in mathematics. Foreign students for whom English is not their native language and who have not completed a bachelor's or master's degree program from an English-speaking university must submit TOEFL scores. While this application is being processed, the student may enter IUPUI as a temporary graduate student. No more than 12 hours of credit earned under this classification may be applied toward an advanced degree. Those who do not want to pursue an advanced degree, but who desire to take graduate courses for personal improvement, may also take courses under the temporary graduate student classification.

Transfer Credit

The Department of Mathematical Sciences will accept by transfer a maximum of 9 hours of graduate credit, in excess of undergraduate degree requirements, from approved institutions.

Assistantships and Fellowships

Financial support is available to qualified students in the form of University Fellowships, graduate teaching assistantships, and tuition scholarships. Additional summer support is available through summer teaching for students whose performance in course work and assistantship duties is satisfactory.

English Requirements

All advanced degree candidates are required to demonstrate acceptable proficiency in English composition.

Foreign students for whom English is not their native language and who have not completed a bachelor's or master's degree program from an English-speaking university must take the ESL exam administered by the IUPUI English as a Second Language Program. Students not scoring sufficiently high will be required to take designated courses in English while pursuing their graduate studies.

Master of Science

A minimum of 30 credit hours of course work is required for an M.S. degree. Course grades must be A or B with the possible exception of at most two grades of C. Neither a thesis nor a comprehensive examination is required. Several core courses are specific to an M.S. plan of study and vary according to the student's interest in

1. pure mathematics with a Ph.D. objective
2. pure mathematics without a Ph.D. objective
3. applied mathematics with a Ph.D. objective
4. applied mathematics without a Ph.D. objective

The remaining courses are selected by the student and his or her advisory committee.

Master of Science (Option for Teachers)

This nonthesis program requires a minimum of 30 credit hours of course work and is tailored for secondary school teachers and students who are preparing to become secondary school teachers. Core requirements include a course in geometry, a course in algebra, a course in analysis, a course in modeling/differential equations, and a course in probability. (See the Department of Mathematical Sciences for a more complete description of this program.) Course grades must be A or B with the possible exception of at most two grades of C.

Master of Science (Concentration in Industrial and Applied Mathematics)

The Master of Science degree with a concentration in Industrial and Applied Mathematics consists of a minimum of 30 credit hours. Course grades must be A or B with the possible exception of at most two grades of C. Candidates for this degree may choose a thesis option, a nonthesis option or an industrial internship option. The nonthesis option requires 18 credit hours in the core curriculum and 12 credit hours in elective courses. The core curriculum consists of two courses in each of the following areas: applied mathematical methods, applied computational methods, and mathematical modeling of physical systems. The elective courses should preferably be in an area of application outside mathematics, unless otherwise approved by the faculty advisor. Both the thesis and the industrial internship option require 18 credit hours in the core curriculum and 6 credit hours in elective courses; the remaining 6 credit hours involve the thesis or the industrial internship work.

Master of Science (Concentration in Applied Statistics)

The Master of Science degree with a concentration in applied statistics consists of a minimum of 30 credit hours. Course grades must be A or B with the possible exception of at most two grades of C. Candidates for this degree may choose either the thesis option or the nonthesis option. Both options require 15 credit hours in the core curriculum consisting of STAT 512, 514, 519, 524, and 528. The two-course sequence in probability and mathematical statistics (STAT 519, 528) must be taken by all degree candidates. A combined written and oral final examination is required.

The nonthesis option consists of 15 credit hours beyond the core curriculum, at least 9 of which must be statistics (STAT) courses. The remaining courses may be taken in mathematics or in areas relevant to statistical applications, subject to approval of the academic advisor.

The thesis option requires a thesis worth 6 credit hours on a topic approved by the candidate's academic advisor. At least 6 of the remaining 9 credit hours must be taken in statistics or in a subject related to statistical applications that has been approved by the advisor. An oral defense of the thesis is required.

Doctor of Philosophy

Qualified students may be authorized to pursue the Ph.D. in mathematics at IUPUI in areas where a program has been arranged with Purdue, West Lafayette. To be admitted to candidacy for the Ph.D. degree, the student must have fulfilled the following requirements and must have been accepted by the graduate committee of the Department of Mathematical Sciences.

Requirements

1. The student must satisfy, by one of the five options approved by the graduate school, the foreign language requirement in German, Russian, or French.
2. The student must pass qualifying examinations in four subject areas: abstract algebra, real analysis, and two additional areas chosen by the student from a list of approved areas. A student may attempt any particular qualifier examination up to three times, but there are time limits imposed by the department for passing all four examinations.
3. The student must submit to the graduate school through the department a plan of study including at least 42 credit hours of approved graduate course work.
4. The student must pass advanced topics examinations. These oral or written examinations may be taken only by students who have completed requirement 2.

A candidate will be recommended to the faculty to receive the Ph.D. degree after a thesis, submitted in final form, has been accepted by the advisory committee and presented before an open colloquium or seminar.

The department has set time limits for completion of the Ph.D. degree.