Although the basic structure of the mathematics major did not change, there were significant changes in the catalog description of the mathematics major in the 1974 – 75 catalog. For the first time, requirements for five emphases (elementary or secondary certification, statistics or actuarial mathematics, computer science, applied mathematics, and pure mathematics) within the mathematics major were given. In addition, the term “cognate requirement” was first used to describe the courses outside of the major that were required for mathematics majors. The need to do this was probably due to the increasing number of mathematics majors seeking certification and the popularity of computer science and statistics for students seeking a career outside of education.

Requirements in the 1974 – 75 catalog

All mathematics majors must complete a minimum of 45 credit hours of mathematics, planned with the approval of a depart­mental faculty adviser. The 45 hours must include

• MTH 201 Calculus and Analytic Geometry I
• MTH 202 Calculus and Analytic Geometry II
• MTH 203 Calculus and Analytic Geometry III
• MTH 225 Linear Algebra I
• MTH 293 Mathematics Colloquium (one credit) or MTH 499 (Independent Study)

At least three courses in the major must be in the College of Arts and Sciences at the 300-level or higher, and at least two of these must be at the 400-level (excluding 499).

The cognate requirement for students seeking a B.S. in mathematics is the completion of one of the following two-course sequences:

• PHY 230 – Principles of Physics I and HSC 435 – History of Mathematics
• PHY 230 – Principles of Physics I and PHY 231 – Principles of Physics II
• ECO 210 – Principles of Economics (Macro) and BUS 490 – Quantitative Business Analysis
• ECO 211 – Principles of Economics (Micro) and BUS 490 – Quantitative Business Analysis

Notice that these are basically the same requirements from the previous year’s catalog. The only difference is the addition of a fourth two-course sequence as an option for the cognate requirements. The emphases within the major basically state how students must complete the remainder of their 45 credits in mathematics.

Elementary or Secondary Certification

Majors who are seeking elementary certification are required are required to take MTH 222 – Concepts of Geometry and Algebra, MTH 341 – Geometry, MTH 345 – Discrete Models, and MTH 420 – Classical Algebra. Majors seeking secondary certification are required to complete MTH 341 - Geometry, MTH 345 – Discrete Models, and MTH 420 – Classical Algebra.

Statistics or Actuarial Mathematics

Majors with this emphasis should include MTH 215 – Statistics I, MTH 216 – Statistics II, MTH 311 – Probability, and MTH 415 – Mathematical Statistics in their programs.

In addition, students interested in statistics should have a good background in computers. Students interested in actuar­ial science should have a good background in business and economics. Many students with this background take one or two of the actuarial exams which are required for working as an actuary in an insurance company. These national exams can be taken on the Grand Valley campus in November and May under the supervision of the Mathematics Department.

Computer Science

Majors with this emphasis should include MTH 152 – Computer Programming in FORTRAN, MTH 252 – Problem Solving Using Computers, MTH 255 – Introduction to Computer Science, MTH 355 – Organization of a Computing System, and MTH 452 – Advanced Computer Project in their programs, and are encouraged to take MTH 153 – Computer Programming in COBOL, MTH 215 – Statistics I, MTH 230 – Mathematical Logic, MTH 345 – Discrete Models, and MTH 405 – Numerical Analysis.

Applied Mathematics

Majors who are seeking careers as mathematicians in industry or governmental agencies should include MTH 152 – Computer Programming in FORTRAN, MTH 215 – Statistics I, MTH 216 – Statistics II, MTH 302 – Ordinary Differential Equations, MTH 405 – Numerical Analysis, and MTH 406 – Applied Mathematical Analysis in their programs.

Pure Mathematics

Majors who plan to do graduate work in pure mathematics should complete MTH 400 – Fundamentals of Analysis, MTH 401 – Real Variables, MTH 402 – Complex Variables, MTH 422 – Algebraic Structures, and MTH 441 – Topology, and study of French, German, or Russian is strongly recommended.

This remained the basic structure for the mathematics major through the 1970’s although some minor changes were made. This continued to the basic structure of the mathematics major even after Grand Valley State Colleges switched from the quarter system to the semester system in 1980.

Although not directly related to the mathematics major, there were some important changes in the Department of Mathematics during this time. In particular,

• The name of the department was changed to the Department of Mathematics and Computer Science in 1976.
• Computer Science became a separate major in 1977, and so was not listed as an emphasis within the mathematics major.
• Two emphases for the computer science major were introduced in 1979. A computer science major was required to complete the Systems Analysis Emphasis or the Information Systems or Data Processing Emphasis. (Note: This was the year that the Computers and Management Program in William James College was discontinued.)
• In 1979, mathematics cognates were added to the requirements for a computer science major. All computer science majors were required to complete MTH 122 – College Algebra, MTH 123 – Trigonometry, MTH 125 – Elementary Analysis or MTH 201 – Calculus and Analytic Geometry I, MTH 215 – Statistics I, and MTH 225 – Finite Mathematics. Note that the name of MTH 225 was changed and it now became a course geared toward computer science students.

Probably the most important change in the mathematics major occurred in 1975 when the department introduced MTH 229 – Mathematical Activities. Following is the description of this course from the 1975 – 76 catalog.

MTH 229 – Mathematical Activities. Techniques of problem-solving using concrete manipu­lative devices and materials. Designed for prospective secondary teachers. Two hours of credit. Prerequisite: Sophomore level or above or consent of instructor. Offered fall term.

It is important to note that this course was a two-credit course at a time when most other courses were 5 credits (in the quarter system). This course became a requirement for the mathematics major with the secondary certification emphasis. There were other changes in the certification emphases, which were made to ensure that prospective teachers had a background in statistics and the use of computers. In addition to the core requirements, the requirements for the Elementary and Secondary Certification Emphases (in the 1975 – 76 catalog) were as follows:

Elementary Certification Emphasis.

• MTH 151 – Computer Programming in BASIC or MTH 152 - Computer Programming in FORTRAN
• MTH 215 – Statistics I
• MTH 222 – Concepts of Geometry and Algebra
• MTH 229 – Mathematical Activities
• MTH 341 – Geometry
• MTH 345 – Discrete Models
• MTH 420 – Classical Algebra

Note: Although technically not part of the major, mathematics majors seeking elementary certification were required to complete MTH 221 – The Real Number System since all students seeking elementary certification were required to complete this course.

Secondary Certification Emphasis.

• MTH 151 – Computer Programming in BASIC or MTH 152 - Computer Programming in FORTRAN
• MTH 229 – Mathematical Activities
• MTH 341 – Geometry
• MTH 345 – Discrete Models
• MTH 420 – Classical Algebra

There were other changes in the mathematics major between 1975 and 1980 and these changes are described below.

• MTH 293 – Problem Solving Seminar was dropped from the curriculum in 1975 and so was no longer required for the mathematics major.
• In 1977, the calculus sequence was changed to four courses. Calculus I and Calculus II remained five-credit courses and remained largely unchanged. Calculus III and Calculus IV were three-credit courses and could be taken simultaneously. Calculus remained a four-course sequence until Grand Valley switched to semesters beginning in the 1980-81 academic year.
• The cognate requirements for the B.S. degree in mathematics were changed a few times during this time period. The main change was to give students more options for completing the cognate requirement. Following are the cognate requirements listed in the 1979 – 80 catalog.

The B.S. degree in mathematics requires a cognate consisting of one of the following two-course sequences:

• BUS 351 – Quantitative Business Analysis and BUS 352. (Note: BUS 352 was not listed in the catalog.)
• ECO 210 – Principles of Economics (Macro) and ECO 313 – Macroeconomic Theory
• ECO 211 – Principles of Economics (Micro) and ECO 312 – Microeconomic Theory
• HSC 435 – History of Mathematics and HSC 399 – Readings in the History of Science
• HSC 435 – History of Mathematics and PHY 230 – Principles of Physics I
• PHY 230 – Principles of Physics I and PHY 231 – Principles of Physics II
• PHY 230 – Principles of Physics I and CHM 356 – Physical Chemistry
• PSY 251 – Introduction to Experimental Methods in Psychology and PSY 351 – Advanced Experimental Methods in Psychology

One other change in the requirements for the major was in the description of the upper-level course requirements. In the 1974 – 75 catalog, it was stated that at least three courses in the major must be in the College of Arts and Sciences at the 300-level or higher, and at least two of these must be at the 400-level (excluding 499). In the 1979 – 80 catalog the description of this requirement was as follows

At least 20 credit hours in the major must be in the College of Arts and Sciences at the 300 level or above and at least five of the 20 credit hours must be at the 400 level, excluding 499. There is one exception: The major who obtains an elementary teaching certificate is required to take 15 credit hours in the College of Arts and Sciences at the 300 level or above and five of the 15 credit hours must be at the 400 level, excluding 499. Such students need not take 203 and 204

An important part of this change is that there are now significant differences between the requirements for the Elementary Certification Emphasis and the other emphases within the major.