# Redesigning the Major - 1998

For the 1988 – 89 academic year, Grand Valley instituted a new general education program. Two new features of this program were:

- A new definition of the B.A. or B.S. degree cognate; and
- The requirement of a capstone course in the major.

The B.S. cognate requirements were quite easy for the department to define, but the department had a difficult time agreeing on an appropriate capstone course for the mathematics major. At that time, the department decided to use MTH 420 – Abstract Algebra as the capstone course for all emphases in the major with the exception of the Statistics and Actuarial Mathematics Emphasis. MTH 415 – Mathematical Statistics II became the capstone course for that emphasis.

In 1993, the Department of Mathematics and Computer Science split into two departments: The Department of Mathematics and Statistics and the Department of Computer Science and Information Systems. At that time, the Department of Mathematics and Statistics decided to make statistics a separate major. Shortly after that decision, the mathematics faculty once again began to consider different possibilities for a capstone course for the mathematics major.

The department began seriously discussing a new capstone course in the 1996 – 97 academic year. Most of this discussion was within a group of mathematics faculty (Ed Aboufadel, Paul Fishback, Salim Haidar, Karen Novotny, Pedro Rivera-Muniz, Steve Schlicker, Ted Sundstrom, Don Vander Jagt, and Clark Wells), but all members of the department were invited to participate in the discussions. It was clear that in the entire major would have to be redesigned in order to create a new capstone course. In the fall of 1997, this group submitted a Program Change Request to the department. This proposal was approved by the department and eventually by the university academic governance. So beginning in 1998, Grand Valley State University had a new mathematics major.

The primary reason for the change in the requirements for the mathematics major was the development of two new capstone courses for the mathematics major. It was felt that although MTH 420 should play a significant role in the major since it deals with important issues in mathematics such as abstraction, axiomatic systems, and algebraic structures. However, since MTH 420 is restricted to only one area of mathematics (algebra), the department had long felt that a better capstone course should be developed. Now, after years of discussion and many attempts at a new capstone, the department felt that it had developed better, more appropriate capstone courses. The two new capstone courses were:

**MTH 495 – The Nature of Modern Mathematics: **

A study of mathematics as a human intellectual endeavor impacting our culture, history, and philosophy. This includes an in-depth investigation, including analyses from the mathematical, historical, and philosophical perspectives, of several significant developments from various fields of mathematics. The specific mathematical developments considered will vary from semester to semester.

**MTH 496 – Senior Thesis**

A senior thesis is written to demonstrate depth and sophistication in the major. Independent library research is conducted under the supervision of a faculty member. Students produce full-fledged, professional, oral and written presentations on this research. Prerequisite: Open to senior mathematics majors in good standing. Consent of instructor required.

The department’s rationale was that the new capstone courses fit the catalog description of a capstone course as “a senior level capstone course aimed at providing the student with a broad and comprehensive perspective on the fundamental assumptions, issues, and problems of the field” exceptionally well, much better than MTH 420. MTH 495 will be a lecture/discussion class in which the diverse content of other mathematics courses would be unified by examining, through historical and philosophical perspectives, issues common to all courses in the major. The majority of mathematics majors were expected to complete MTH 495 as their capstone course.

In keeping with recent emphasis at Grand Valley on independent student work and student research, the department offered MTH 496 as an alternative to MTH 495. It was felt that MTH 496 would be beneficial to those students who wished to pursue independent work in areas of mathematics of their own choosing.

**Other Changes in the Requirements for the Major**

The development of these new capstone courses made possible a rearrangement of courses and requirements for the major. Following is a description of these changes along with a brief rationale for each change.

**1. The Modern Algebra Sequence**

Although it was a valuable course, the department felt that MTH 420 was a bit too abstract and too removed from direct, obvious application to students in our certification programs. With a new capstone course in place, MTH 420 (Abstract Algebra I) was revised. This revised algebra course, MTH 310 (Modern Algebra I) was more focused on the development of familiar number systems (rational, real, and complex numbers) than is MTH 420 since it was felt that the development of number systems is directly related to topics with which future teachers will work in their classrooms. In addition, the constructions used in developing the familiar number systems lend themselves quite easily to more abstract systems, allowing for a more natural transition to abstract structures. Since MTH 310 dealt less with abstract structures than with specific ones, the title was changed to Modern Algebra. It was felt that this course would serve those in the secondary certification and elementary certification programs, better than MTH 420 did. This course would be required of all majors.

In changing MTH 420 to MTH 310, it was also necessary to alter the subsequent course, MTH 422 (Abstract Algebra II) as well. The old MTH 420 and MTH 422 formed a year long sequence in abstract algebra. The department wished to maintain this sequence and, as a result, renumbered MTH 422 to MTH 410. The changes in this course were slight, allowing for the fact that students will exit MTH 310 with less experience with abstract structures than they did from MTH 420. This course, MTH 410, was not to be a required course, but would be part of one option for a year long sequence required in the new major.

**2. A Year Long Sequence of Upper Level Courses**

Since the department believed in was important that each mathematics major acquires an in-depth knowledge of some area of mathematics, one of the new requirements in the major was that each student was required to complete a year long sequence of upper level courses in the major. The sequences identified were MTH 310, 410 (Modern Algebra), MTH 408, 409 (Advanced Calculus), MTH 341, 431 (Geometry), MTH 300, 400 (Applied Analysis), and MTH 345, MTH 360 (Discrete Mathematics and Applications). However, students seeking elementary certification would be required to complete the three-course sequence MTH 321, MTH 322, and MTH 323 since these three courses formed a sequence of upper level mathematics courses intended specifically for prospective elementary teachers. Different emphases in the majors would require different upper-level sequences.

**3. The Pregraduate Mathematics and Applied Mathematics Emphases**

These two emphases were eliminated. It was felt that the it would be better to explain options for these students through advising.

Majors who planned to do graduate work in mathematics would be encouraged to: (i) take as many upper-division mathematics courses from the courses listed above as possible; (ii) complete at least one of the two-course upper level sequences in Modern Algebra or Advanced Calculus; (iii) consult with their advisor about other courses that might be appropriate for their interests and about procedures for applying to graduate school; and (iv) complete a B.A. degree by completing the third semester of French, German, or Russian.

Majors interested in applied mathematics would be advised to take MTH 304, MTH 300 and MTH 400 (or MTH 345 and MTH 360), MTH 405, PHY 230, and STA 216.

**4. Cognates for the Mathematics Major**

In the past, the cognate requirements for the major had been specific, computer science (CS 162 - Computer Science I) and physics (PHY 230 - Principles of Physics). Recognizing that there are many other areas in which mathematics is used, the department desired to encourage our students to explore these areas by expanding the possibilities for cognate courses. The department identified courses offered by other departments that had a significant mathematics prerequisite and that could potentially fit into a minor program. The cognate requirements depended on the emphasis chosen by the student. See the requirements for mathematics major at the end of this document.

**5. The B.S. Cognates for the Mathematics Major**

The B.S. cognate requirements for a mathematics major at that time was MTH 201 (Calculus and Analytic Geometry I), MTH 202 (Calculus and Analytic Geometry II), and PHY 230 (Principles of Physics I). In the proposed mathematics major, PHY 230 was no longer a required cognate for our major. (It was one option to satisfy the cognate requirement for the major.) Consequently, a change was needed in the B.S. cognate for the mathematics major.

The proposed new B.S. cognate requirements for the mathematics major were MTH 201 (Calculus and Analytic Geometry I), MTH 202 (Calculus and Analytic Geometry II), and STA 312 (Probability and Statistics). One of the university requirements for the B.S. cognate was that at least one of the three courses had to be from a discipline outside of the major. So an argument was needed that a statistics was such a course. The argument was basically that for a long time, it was unusual for a statistics course to be required within a mathematics since in fact, statistics is a very different discipline than mathematics and is not a subfield of mathematics. Statistics is the methodological field that deals with collecting data, organizing and summarizing data, and drawing conclusions from data. It was also argued that the inclusion of a statistics course in the mathematics major was consistent with recommendations made by the Mathematical Association of America and that a basic understanding of statistics was becoming increasingly important for educated citizens, especially teachers since concepts of statistics were becoming increasingly taught in schools.

**New Requirements for the Mathematics Major**

One of the issues that the department had to deal with was that a new major should not significantly increase the number of credits for a mathematics major. The University Curriculum Committee scrutinized program change proposals closely with respect to this matter. The new major, including cognates, required approximately the equivalent of one more course than the previous requirements for the major. Following are the requirements for the mathematics major that were approved for the 1998 – 99 academic year.

1. University degree requirements as identified in the General Academic Regulations section of the catalog.

2. Mathematics Core

All mathematics majors must complete the following courses

MTH 201 Calculus and Analytic Geometry I 5 credits

MTH 202 Calculus and Analytic Geometry II 4 credits

MTH 210 Communicating in Mathematics 3 credits

MTH 227 Linear Algebra I 3 credits

MTH 310 Modern Algebra I 3 credits

MTH 495 Nature of Modern Mathematics

or MTH 496 Senior Thesis 3 credits

3. In addition to the core, students who are not seeking teacher certification must complete the following requirements:

a. Required Mathematics courses:

MTH 203 Calculus and Analytic Geometry III 4 credits

MTH 408 Advanced Calculus I 3 credits

b. One of the following upper level two course sequences:

MTH 310 and MTH 410 (Modern Algebra)

MTH 408 and MTH 409 (Advanced Calculus)

MTH 341 and MTH 431 (Geometry)

MTH 300 and MTH 400 (Applied Analysis)

MTH 345 and MTH 360 (Discrete Mathematics and Applications)

c. Additional course(s) from the following list for a total of 37 credits in mathematics:

300, 304, 327, 341, 345, 360, 400, 402, 405, 409, 410, 431, 441, 465

d. Cognate Requirements

STA 312 – Probability and Statistics;

CS 162 – Computer Science I;

One course from the following:

PHY 230 – Principles of Physics I

ECO 480 – Econometrics and Forecasting

GEO 440 – Geohydrology

GEO 470 – Geophysics

STA 314 – Statistical Quality Methods

STA 316 – Advanced Applied Statistics

STA 412 – Mathematical Statistics I

SS 300 – Research Methods in the Social Sciences

BIO 355 – Human Genetics

BIO 375 – Genetics

CHM 351 – Introduction to Physical Chemistry

Note: Completion of MTH 201, MTH 202, and STA 312 satisfies the B.S. degree cognate for all mathematics majors. Students completing a B.A. degree must complete these courses plus the foreign language requirement for a B.A.

4. Elementary Certification Emphasis

A minimum GPA of 2.8 is required in the major for recommendation for teacher certification. In addition to the core, students who are seeking a mathematics major with elementary certification must complete the following requirements:

a. Required Mathematics Courses

MTH 321 Number Systems and Structures 3 credits

MTH 322 Geometry for Elem. Teachers 3 credits

MTH 323 Stat. and Prob. for Elem. Teachers 3 credits

MTH 341 Euclidean Geometry 3 credits

MTH 345 Discrete Mathematics 3 credits

b. Cognate requirements

STA 312 – Probability and Statistics;

One course from the following:

PHY 220 – General Physics I

PHY 230 – Principles of Physics I

CS 160 – Programming with Visual Basic

CS 162 – Computer Science I

ECO 480 – Econometrics and Forecasting

GEO 440 – Geohydrology

GEO 470 – Geophysics

STA 314 – Statistical Quality Methods

STA 316 – Advanced Applied Statistics

STA 412 – Mathematical Statistics I

SS 300 – Research Methods in the Social Sciences

BIO 355 – Human Genetics

BIO 375 – Genetics

CHM 351 – Introduction to Physical Chemistry

c. School of Education requirements for elementary certification must also be met.

5. Secondary Certification Emphasis

A minimum GPA of 2.8 is required in the major for recommendation for teacher certification. In addition to the core, students who are seeking a mathematics major with secondary certification must complete the following requirements:

a. Required Mathematics Courses

MTH 203 Calculus and Analytic Geometry III 4 credits

MTH 229 Math. Act. for Sec. Teachers 3 credits

MTH 341 Euclidean Geometry 3 credits

MTH 345 Discrete Mathematics 3 credits

MTH 410 Modern Algebra II

or MTH 431 Non-Euclidean Geometry 3 credits

b. One additional course from the following list:

300, 304, 327, 360, 400, 402, 405, 408, 409, 410, 431, 441, 465

c. Cognate Requirements

STA 312;

One course from the following:

PHY 230 – Principles of Physics I

CS 162 – Computer Science I

ECO 480 – Econometrics and Forecasting

GEO 440 – Geohydrology

GEO 470 – Geophysics

STA 314 – Statistical Quality Methods

STA 316 – Advanced Applied Statistics

STA 412 – Mathematical Statistics I

SS 300 – Research Methods in the Social Sciences

BIO 355 – Human Genetics

BIO 375 – Genetics

CHM 351 – Introduction to Physical Chemistry