# Mathematics Major - 1988 to 1998

Except for the introduction of the B.S. degree cognate, the capstone course in the major, and some minor rewriting for clarification, the requirements for a mathematics major did not change in 1987.

- The Mathematics Core now consisted of the three courses in the calculus sequence, MTH 227 – Linear Algebra I, MTH 235 – Communicating in Mathematics, and a capstone course (MTH 415 – Mathematical Statistics I or MTH 420 – Abstract Algebra).
- All majors were still required to complete PHY 230 – Principles of Physics I and either CS 151 – Introduction to Programming or CS 152 – Programming in FORTRAN.
- The upper level requirement now stated that at least an additional 14 credits in mathematics were required to accumulate 36 credits in mathematic and that at least three additional courses in the major must be mathematics courses at the 300 level or above.
- The optional emphases were still the Statistics or Actuarial Mathematics Emphasis, the Elementary or Secondary Certification Emphasis, the Applied Mathematics Emphasis, and the Pregraduate Mathematics Emphasis.
- MTH 215 – Statistics I could be included in the all emphases except the Pregraduate Mathematics Emphasis.
- MTH 222 – Mathematics for Elementary Teachers II could only be included for a major who obtains an elementary teaching certificate.
- Majors seeking elementary teaching certificates were allowed to substitute CS 140 – Computer Programming in BASIC for CS 151 or CS 152 and could substitute PHY 220 – General Physics I for PHY 230. (PHY 220 did not have a calculus prerequisite.)

Although there were changes made to various parts of the mathematics majors and to some of the emphases within the major, the basic structure of the mathematics major did not change until 1998. In particular, MTH 415 – Mathematical Statistics I and MTH 420 – Abstract Algebra continued to be the capstone courses. Following are descriptions of some of the more significant changes in the mathematics major between 1988 and 1998.

**A New Statistics Course for the Mathematics Major**

Since 1975, the department had required mathematics majors seeking elementary certification to complete a statistics course, namely MTH 215 – Statistics I. It was not until 1985 that mathematics majors seeking secondary certification were required to take MTH 215. Shortly after that, members of the department began discussing whether or not MTH 215 was an appropriate course for mathematics majors. In particular, it was felt that although MTH 215 was a good course, its target audience was really general education students with much less mathematical background than mathematics majors. The prerequisite for MTH 215 was MTH 110 – Algebra, and consequently, in order to make the course appropriate for students with this mathematical background, the department could not teach MTH 215 in a way that sufficiently challenged mathematics majors.

So in the fall of 1987, the department approved a new statistics course, MTH 312 – Probability and Statistics, that was designed to introduce students to view probability and statistics using calculus. The prerequisite for this course was the first course in the calculus sequence, and hence, the course was intended for mathematics majors who could appreciate a deeper understanding of the concepts of probability and statistics with the aid of their stronger background in mathematics. This course became a requirement for all emphases in the major except the Pregraduate Mathematics Emphasis.

Note: The department had a “numbering problem” for this course. Statistics I and Statistics II were numbered 215 and 216, and it had to be the case that the prerequisite for MTH 216 would be MTH 215 or MTH 312. The only way to avoid the problem of having a higher numbered course (MTH 312) serve as a prerequisite for a lower numbered course (MTH 216) was to completely renumber the statistics courses, and the department decided not to do this.

**Changes in the Statistics or Actuarial Mathematics Emphasis**

There were some small changes in the Statistics or Actuarial Mathematics emphasis for the 1990 – 91 catalog, and in reality, the changes were made to clarify the requirements for this emphasis. Since the advent of a capstone course in the major in 1987, the catalog stated that one of the requirements for this emphasis was the completion of MTH 316 – Statistics III or MTH 415 – Mathematical Statistics II. In reality, of course, students needed to complete MTH 415 as their capstone course. So the requirements for the Statistics or Actuarial Mathematics Emphasis were changed so that students in this emphasis were required to complete the following:

- MTH 216 – Statistics II
- MTH 312 – Probability and Statistics
- MTH 316 – Statistics III
- MTH 412 – Mathematical Statistics I
- MTH 415 – Mathematical Statistics II
- One other approved course.

Note: The number for Mathematical Statistics I had been changed from MTH 315 to MTH 412 for the 1989 – 90 catalog.

**Changes in the Differential Equations Courses**

Grand Valley State opened a School of Engineering in 1987 and began offering a B.S.E. degree. Prior to that time, a B.S. in Engineering Science was offered through the Department of Physics. When it began, the mathematics requirements for the B.S.E. degree were the three courses in the calculus sequence, MTH 227 – Linear Algebra I, and MTH 302 – Ordinary Differential Equations. (This was a total of 20 credits in mathematics.)

One of the issues facing the new School of Engineering was accreditation by ABET (Accreditation Board for Engineering and Technology) and trying to design a curriculum to meet ABET standards. In 1989, the School of Engineering approached the Department of Mathematics and Computer Science with a proposal to assist in the accreditation process. This proposal was basically to develop a new course that combined basic linear algebra and ordinary differential equations, which engineering students would take instead of MTH 227 and MTH 302. This would reduce the number of credits in mathematics required for engineering students from 20 to 17. In order to reduce confusion between “old” and “new” courses in the accreditation process, the decision was to propose the following:

- Change the then current MTH 302 to MTH 304 – Analysis of Differential Equations. The prerequisites for this course would be Calculus III and Linear Algebra I.
- Develop a new course, MTH 302 – Linear Algebra and Differential Equations, specifically designed for engineering. The prerequisite for this course would be Calculus III.

One of the issues that the department needed to address with these proposals was the overlap in content between the two courses. The department felt it was essential that a separate linear algebra course be required for all mathematics majors and that if they chose to take a differential equations courses (required in the Applied Mathematics Emphasis), a combined course in linear algebra and differential equations would be inappropriate.

These proposals, of course, were supported by the School of Engineering. However, the Department of Physics expressed some concern about these proposals. The main concern was that the proposed changes would make it more difficult for students to change majors between engineering, physics, and mathematics. In late 1989, a meeting was held with representatives of the programs involved, and an agreement was reached and eventually the proposals were approved for the 1990 – 91 catalog. Following are the catalog descriptions of the two courses.

**MTH 302 Linear Algebra and Differential Equations. **Matrix algebra and determinants. Introduction to the theory of differential equations. Methods of solution (including Laplace transform techniques) of linear equations as well as some special types of non-linear equations. Applications in physical, biological, and social sciences. Prerequisite: 203. Four credits.

**MTH 304 Analysis of Differential Equations. **Solution methods for first order and second order linear equations (including power series and numerical methods). The linear algebra of linear systems and their solutions. Qualitative analysis of linear and non-linear systems: phase plane; existence and uniqueness; stability, applications in physical, biological, and social sciences. Prerequisites: 203 and 227. Four credits.

MTH 304 was changed to a three-credit course the following year.

**Advanced Calculus and the Requirements for the Pregraduate Mathematics Emphasis**

For quite some time, the only description of the requirements for the Pregraduate Mathematics Emphasis was that, “Majors who plan to do graduate work in mathematics should consult with their advisors to enroll in appropriate courses and independent studies.” The requirements for this emphasis were made more explicit for the 1991 – 92 catalog.

The year prior to that, the department had introduced two new courses in the mathematics curriculum. These were MTH 303 – Advanced Calculus I and MTH 403 – Advanced Calculus II. Prior to this, students planning on going to graduate work usually took these courses as independent studies, which was difficult on both the students and the faculty. Since more students were now considering graduate school as an option, and in an effort to attract more such students, the department felt it necessary to have a traditional advanced calculus sequence in the curriculum. With these courses now in the catalog, the department approved the following requirements for the Pregraduate Mathematics Emphasis for the 1991 – 92 catalog.

Majors who plan to do graduate work in mathematics are encouraged to take as many upper-division mathematics courses from the following list as possible, including at least one of the two one-year-long sequences in Advanced Calculus or Abstract Algebra.

- MTH 303 Advanced Calculus I and MTH 403 Advanced Calculus II.
- MTH 304 Analysis of Differential Equations.
- MTH 327 Linear Algebra II.
- MTH 345 Discrete Structures II.
- MTH 402 Complex Variables.
- MTH 420 Abstract Algebra I and MTH 422 Abstract Algebra II.
- MTH 441 Topology.

Majors with this emphasis should consult their advisor about other courses! that might be appropriate for their interests and about procedures for applying to graduate school. For this emphasis, it is also recommended that students complete a B.A. degree by completing the third semester of French, German, or Russian.

**New Courses and the Elementary Certification Emphasis**

One small change in the Elementary Certification Emphasis occurred in 1989 when a new course, CS 130 – Problem Solving in LOGO, was introduced. This then became a course that students with this emphasis could use as their computer science course in the cognate requirements for the mathematics major.

One of the most significant changes in the major during this time was the redesign of the Elementary Certification Emphasis. For quite some time, there had been differences between this emphasis and other emphases in the major. For example, since 1975, students seeking elementary certification could include MTH 215 – Statistics I and MTH 222 – Mathematics for Elementary Teachers II in their major and students in other emphases could not do so. Also, since 1977, mathematics majors seeking elementary certification were not required to take Calculus III.

The major change was to put three new courses into this emphasis. These courses were designed specifically for this emphasis. These courses were:

- MTH 321 – Number Systems and Structure;
- MTH 322 – Geometry for Elementary Teachers; and
- MTH 323 – Probability and Statistics for Elementary Teachers.

Note: In 2006, MTH 321 was renumbered and renamed to be MTH 324 – Algebra for Elementary Teachers.

These changes were made in this emphasis because of national education organizations, such as the National Council of Teachers of Mathematics, were proposing major changes in how and what prospective elementary teachers are taught, and these courses followed these new national guidelines closely. Following are the requirements for the Mathematics Major with an Elementary Certification Emphasis from the 1992 – 93 catalog:

A minimum GPA of 2.5 is required in the major for recommendation for teacher certification. Students with this emphasis need not take MTH 203. Majors seeking elementary certification are also required to complete:

- MTH 321 Number Systems and Structures.
- MTH 322 Geometry for Elementary Teachers.
- MTH 323 Statistics and Probability for Elementary Teachers.
- MTH 341 Geometry.
- MTH 345 Discrete Structures II.
- MTH 420 Abstract Algebra I.

One additional approved course.

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

To be approved for student teaching, students must complete at least 24 semester hours of courses in the major, including 235, and at least two of 321,322, and 323.

Students may substitute PHY 220 – General Physics I for PHY 230 – Principles of Physics I, and CS 130 – Problem Solving with LOGO or CS 140 – Computer Programming in BASIC may be substituted for CS 151 – Computer Science I in the cognate requirements,

**Some Other Changes**

Although it did not affect the requirements for a major in mathematics, in 1993, the Department of Mathematics and Computer Science was dissolved and two new departments were formed, which were

- 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, and consequently, the Statistics and Actuarial Mathematics Emphasis in the mathematics major was eliminated.

Also, at that time, the Department of Computer Science and Information Systems restructured its curriculum. One change was to renumber the first course in the computer science major from CS 151 to CS 162. So the cognate requirements in mathematics now listed CS 162 – Computer Science I as one choice for a computer science course. Also, in 1995, the Department of Computer Science dropped the course CS 152 – Programming in FORTRAN, and so this course was no longer an option in the cognate requirements for a mathematics major.