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# 2020-2021 Undergraduate & Graduate Catalog

## Bachelor of Arts or Bachelor of Science in Mathematics

- Requirements for a Major in Mathematics - Theoretical Mathematics Emphasis
- Requirements for a Major in Mathematics - Applied Mathematics Emphasis
- Requirements for a Major in Mathematics - Elementary Certification Emphasis
- Requirements for a Major in Mathematics - Secondary Certification Emphasis
- Suggested Order of Coursework for a Major in Mathematics

### Emphasis Areas

Students majoring in mathematics must choose one of the following emphasis areas:

- Theoretical mathematics
- Applied mathematics
- Elementary certification
- Secondary certification

### B.S. and B.A. Degree Requirements

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

### Requirements for a Major in Mathematics - Theoretical Mathematics Emphasis

Students planning a major in mathematics with theoretical mathematics emphasis must complete the following.

#### Course Requirements

All students with a major in mathematics with theoretical mathematics emphasis must complete the following courses:

- MTH 201 - Calculus I (4 credits)
- MTH 202 - Calculus II (4 credits)
- MTH 203 - Calculus III (4 credits)
- MTH 204 - Linear Algebra I (3 credits)
- MTH 205 - Linear Algebra II (3 credits)
- MTH 210 - Communicating in Mathematics (4 credits)
- MTH 350 - Modern Algebra I (3 credits)
- MTH 408 - Real Analysis 1 (3 credits)
- MTH 495 - The Nature of Modern Mathematics (Capstone) (3 credits)
**OR**MTH 496 - Senior Thesis (Capstone) (3 credits)

#### Additional Course Requirements

Take additional courses from the following list for a total of 12 courses in mathematics (with at least one additional 400-level course besides the required courses):

- MTH 300 - Vector Analysis (3 credits)
- MTH 304 - Analysis of Differential Equations (3 credits)
- MTH 305 - Mathematical Modeling (3 credits)
- MTH 315 - Discrete Mathematics (3 credits)
- MTH 360 - Operations Research (3 credits)
- MTH 401 - Mathematics for the Physical Sciences (4 credits)
- MTH 402 - Complex Variables (3 credits)
- MTH 405 - Numerical Analysis (3 credits)
- MTH 406 - Linear Algebra III (3 credits)
- MTH 409 - Real Analysis 2 (3 credits)
- MTH 431 - Non-Euclidean Geometry (3 credits)
- MTH 441 - Topology (3 credits)
- MTH 450 - Modern Algebra II (3 credits)
- MTH 465 - Automata and Theory of Computation (3 credits)
- MTH 495 - The Nature of Modern Mathematics (Capstone) (3 credits)
- MTH 496 - Senior Thesis (Capstone) (3 credits)
- MTH 498 - Project-Based Applied Mathematics (Capstone) (3 credits)

#### Cognate Requirements

All students seeking a major in mathematics with theoretical mathematics emphasis must complete the following courses to satisfy the mathematics cognate requirements:

- CIS 161 - Computational Science (3 credits) Recommended.

**OR**CIS 162 - Computer Science I (4 credits)**OR**CIS 261 - Structured Programming in C (3 credits) - STA 312 - Probability and Statistics (3 credits)

**AND** one course from the following:

- BIO 355 - Human Genetics (3 credits)
- BIO 375 - Genetics (3 credits)
- CHM 351 - Introduction to Physical Chemistry (3 credits)
- CMB 451 - Bioinformatics: Tools and Techniques for Life Scientists (3 credits)
- CMB 452 - Computer Modeling of Biomolecules (3 credits)
- ECO 400 - Econometrics and Forecasting (3 credits)
- GEO 470 - Geophysics (4 credits)
- HSC 201 - The Scientific Revolution (3 credits)
- PHI 203 - Intermediate Logic (3 credits)
- PHY 230 - Principles of Physics I (5 credits)
- PSY 300 - Research Methods in Psychology (3 credits)
- STA 314 - Statistical Quality Methods (3 credits)
- STA 412 - Mathematical Statistics I (4 credits)

### Preparation for Graduate Work in Theoretical Mathematics

Majors who plan to complete graduate work in mathematics are encouraged to

- take as many upper-division mathematics courses as possible from the courses listed in additional mathematics courses;
- take MTH 450 or MTH 409 as one additional 400-level course; and
- consult with their advisor about other courses that might be appropriate for their interests and about procedures for applying to graduate school.

### Requirements for a Major in Mathematics - Applied Mathematics Emphasis

Students planning a major in mathematics with applied mathematics emphasis must complete the following.

#### Course Requirements

All students with a major in mathematics with applied mathematics emphasis must complete the following courses:

- MTH 201 - Calculus I (4 credits)
- MTH 202 - Calculus II (4 credits)
- MTH 203 - Calculus III (4 credits)
- MTH 204 - Linear Algebra I (3 credits)
**AND**MTH 304 - Analysis of Differential Equations (3 credits) Recommended.**OR**only MTH 302 - Linear Algebra and Differential Equations (4 credits) - MTH 205 - Linear Algebra II (3 credits)
- MTH 210 - Communicating in Mathematics (4 credits)
- MTH 305 - Mathematical Modeling (3 credits)
- MTH 360 - Operations Research (3 credits)
- MTH 405 - Numerical Analysis (3 credits)
- MTH 490 - Mathematics Internship Seminar (2 credits) Capstone
**OR**MTH 498 - Project-Based Applied Mathematics (Capstone) (3 credits)

#### Additional Course Requirements

Take additional courses from the following list for a total of 13 courses in mathematics. Students choosing the recommended MTH 204 + MTH 304 option in the required courses, must take two additional courses from the following list, while the students choosing only MTH 302 must take three additional courses from the following list:

- MTH 315 - Discrete Mathematics (3 credits)
- MTH 401 - Mathematics for the Physical Sciences (4 credits)
- MTH 402 - Complex Variables (3 credits)
- MTH 406 - Linear Algebra III (3 credits)
- MTH 408 - Real Analysis 1 (3 credits)
- MTH 441 - Topology (3 credits)
- MTH 465 - Automata and Theory of Computation (3 credits)
- MTH 496 - Senior Thesis (Capstone) (3 credits)
- MTH 498 - Project-Based Applied Mathematics (Capstone) (3 credits)

#### Cognate Requirements

All students seeking a major in mathematics with applied mathematics emphasis must complete the following courses to satisfy the mathematics cognate requirements:

- CIS 161 - Computational Science (3 credits) Recommended.

**OR**CIS 162 - Computer Science I (4 credits)**OR**CIS 261 - Structured Programming in C (3 credits) - STA 312 - Probability and Statistics (3 credits)

### Requirements for a Major in Mathematics - Elementary Certification Emphasis

The mathematics major with elementary certification emphasis must be completed with a GPA of 2.7 for admission to the College of Education. Students planning a major in mathematics with elementary certification emphasis must complete the following requirements.

#### Course Requirements

All students with a major in mathematics with elementary certification emphasis must complete the following courses:

- MTH 201 - Calculus I (4 credits)
- MTH 202 - Calculus II (4 credits)
- MTH 204 - Linear Algebra I (3 credits)
- MTH 210 - Communicating in Mathematics (4 credits)
- MTH 315 - Discrete Mathematics (3 credits)
- MTH 322 - Geometry for Elementary Teachers (3 credits)
- MTH 323 - Probability and Statistics for Elementary Teachers (3 credits)
- MTH 324 - Algebra for Elementary Teachers (3 credits)
- MTH 331 - Euclidean Geometry (3 credits)
- MTH 350 - Modern Algebra I (3 credits)
- MTH 495 - The Nature of Modern Mathematics (Capstone) (3 credits)
**OR**MTH 496 - Senior Thesis (Capstone) (3 credits)

#### Cognate Requirements

All students seeking a major in mathematics with elementary certification emphasis must complete the following courses to satisfy the mathematics cognate requirements:

**AND** one course from the following:

- BIO 355 - Human Genetics (3 credits)
- BIO 375 - Genetics (3 credits)
- CHM 351 - Introduction to Physical Chemistry (3 credits)
- CIS 160 - Learn to Code in Python (3 credits)
- CIS 161 - Computational Science (3 credits)
- CIS 162 - Computer Science I (4 credits)
- CIS 261 - Structured Programming in C (3 credits)
- CMB 451 - Bioinformatics: Tools and Techniques for Life Scientists (3 credits)
- CMB 452 - Computer Modeling of Biomolecules (3 credits)
- ECO 400 - Econometrics and Forecasting (3 credits)
- GEO 470 - Geophysics (4 credits)
- HSC 201 - The Scientific Revolution (3 credits)
- PHI 203 - Intermediate Logic (3 credits)
- PHY 220 - General Physics I (5 credits)
- PHY 230 - Principles of Physics I (5 credits)
- PSY 300 - Research Methods in Psychology (3 credits)
- SCI 226 - Integrated Physical Science for K-8 Teachers (3 credits) Recommended.
- STA 314 - Statistical Quality Methods (3 credits)
- STA 345 - Statistics in Sports (3 credits)
- STA 412 - Mathematical Statistics I (4 credits)

#### College of Education Requirements

To be approved for student teaching, students must complete at least 24 credit hours in the major, including:

**AND** at least two of the following:

- MTH 322 - Geometry for Elementary Teachers (3 credits)
- MTH 323 - Probability and Statistics for Elementary Teachers (3 credits)
- MTH 324 - Algebra for Elementary Teachers (3 credits)

In addition, students need to be aware of the College of Education requirements for admission to the elementary certification program.

### Requirements for a Major in Mathematics - Secondary Certification Emphasis

The mathematics major with secondary certification emphasis must be completed with a GPA of 2.7 for admission to the College of Education. Students planning a major in mathematics with secondary certification emphasis must complete the following.

#### Course Requirements

All mathematics majors must complete the following courses:

- MTH 201 - Calculus I (4 credits)
- MTH 202 - Calculus II (4 credits)
- MTH 203 - Calculus III (4 credits)
- MTH 204 - Linear Algebra I (3 credits)
- MTH 210 - Communicating in Mathematics (4 credits)
- MTH 229 - Mathematical Activities for Secondary Teachers (3 credits)
- MTH 315 - Discrete Mathematics (3 credits)
- MTH 329 - Teaching Middle Grades Mathematics (3 credits)
- MTH 331 - Euclidean Geometry (3 credits)
- MTH 350 - Modern Algebra I (3 credits)
- MTH 495 - The Nature of Modern Mathematics (Capstone) (3 credits)
**OR**MTH 496 - Senior Thesis (Capstone) (3 credits)

#### Elective Requirement

All mathematics majors with secondary certification emphasis must also complete one elective course from the following list. The elective course must be different than the Capstone course.

- MTH 205 - Linear Algebra II (3 credits)
- MTH 300 - Vector Analysis (3 credits)
- MTH 304 - Analysis of Differential Equations (3 credits)
- MTH 360 - Operations Research (3 credits)
- MTH 401 - Mathematics for the Physical Sciences (4 credits)
- MTH 402 - Complex Variables (3 credits)
- MTH 405 - Numerical Analysis (3 credits)
- MTH 408 - Real Analysis 1 (3 credits)
- MTH 409 - Real Analysis 2 (3 credits)
- MTH 431 - Non-Euclidean Geometry (3 credits)
- MTH 441 - Topology (3 credits)
- MTH 450 - Modern Algebra II (3 credits)
- MTH 465 - Automata and Theory of Computation (3 credits)
- MTH 495 - The Nature of Modern Mathematics (Capstone) (3 credits)
- MTH 496 - Senior Thesis (Capstone) (3 credits)

#### Cognate Requirements

All students seeking a major in mathematics with secondary certification emphasis must complete the following courses to satisfy the mathematics cognate requirements:

**AND **one course from the following:

- BIO 355 - Human Genetics (3 credits)
- BIO 375 - Genetics (3 credits)
- CHM 351 - Introduction to Physical Chemistry (3 credits)
- CIS 160 - Learn to Code in Python (3 credits)
- CIS 161 - Computational Science (3 credits)
- CIS 162 - Computer Science I (4 credits)
- CIS 261 - Structured Programming in C (3 credits)
- CMB 451 - Bioinformatics: Tools and Techniques for Life Scientists (3 credits)
- CMB 452 - Computer Modeling of Biomolecules (3 credits)
- ECO 400 - Econometrics and Forecasting (3 credits)
- GEO 470 - Geophysics (4 credits)
- HSC 201 - The Scientific Revolution (3 credits)
- PHI 203 - Intermediate Logic (3 credits)
- PHY 230 - Principles of Physics I (5 credits)
- PSY 300 - Research Methods in Psychology (3 credits)
- STA 314 - Statistical Quality Methods (3 credits)
- STA 345 - Statistics in Sports (3 credits)
- STA 412 - Mathematical Statistics I (4 credits)

#### College of Education Requirements

To be approved for student teaching, students must complete at least 24 credit hours in the major, including:

- MTH 210 - Communicating in Mathematics (4 credits)
- MTH 229 - Mathematical Activities for Secondary Teachers (3 credits)
- MTH 331 - Euclidean Geometry (3 credits)

In addition, students need to be aware of the College of Education requirements for admission to the secondary certification program.

A student who has graduated from another accredited institution with a completed major or minor in mathematics and who now seeks only teaching certification in mathematics from Grand Valley must satisfy the following criteria:

- Transfer or complete at Grand Valley all mathematics and cognate courses required for the certification major or minor.
- A minimum cumulative GPA of 2.7 (on a 4.0 scale) in mathematics courses from the accredited institution.
- Completion of the College of Education requirements for certification.

### Suggested Order of Coursework for a Major in Mathematics

The following sample mathematics schedules assume the student is in contact with an advisor for appropriate general education requirements and has a strong mathematics background. Students who do not begin with MTH 201 will need to make appropriate changes.

#### Mathematics Majors with Theoretical Mathematics Emphasis

**Year One**

- Appropriate courses in general education
- MTH 201 - Calculus I (4 credits)
- MTH 202 - Calculus II (4 credits)
- MTH 204 - Linear Algebra I (3 credits)
- MTH 205 - Linear Algebra II (3 credits)

**Year Two**

- Mathematics elective course
- Computer science cognate course
- Appropriate courses in general education
- MTH 203 - Calculus III (4 credits)
- MTH 210 - Communicating in Mathematics (4 credits)

**Year Three**

- Cognate courses in the major
- Appropriate courses in general education
- Mathematics elective course
- MTH 350 - Modern Algebra I (3 credits)
- STA 312 - Probability and Statistics (3 credits)

**Year Four**

- 400-level mathematics elective course
- Capstone course
- MTH 408 - Real Analysis 1 (3 credits)

#### Mathematics Majors with Applied Mathematics Emphasis

**Year One**

- Appropriate courses in general education
- MTH 201 - Calculus I (4 credits)
- MTH 202 - Calculus II (4 credits)
- MTH 204 - Linear Algebra I (3 credits)
- MTH 205 - Linear Algebra II (3 credits)

**Year Two**

- Computer science cognate course
- Appropriate courses in general education
- MTH 203 - Calculus III (4 credits)
- MTH 210 - Communicating in Mathematics (4 credits)
- MTH 304 - Analysis of Differential Equations (3 credits)

**Year Three**

- Mathematics elective course
- Appropriate courses in general education
- MTH 305 - Mathematical Modeling (3 credits)
- MTH 360 - Operations Research (3 credits)
- STA 312 - Probability and Statistics (3 credits)

**Year Four**

- Mathematics elective course
- Capstone course
- MTH 405 - Numerical Analysis (3 credits)

#### Mathematics Major with Elementary Certification Emphasis

**Year One**

- Appropriate course in general education
- MTH 201 - Calculus I (4 credits)
- MTH 202 - Calculus II (4 credits)
- MTH 210 - Communicating in Mathematics (4 credits)
- PSY 101 - Introductory Psychology (3 credits)

**Year Two**

- Appropriate courses in general education
- MTH 204 - Linear Algebra I (3 credits)
- MTH 315 - Discrete Mathematics (3 credits)
- MTH 322 - Geometry for Elementary Teachers (3 credits)
- STA 312 - Probability and Statistics (3 credits)

**Year Three**

- Student assisting
- Cognate course for major
- Appropriate course in general education
- MTH 323 - Probability and Statistics for Elementary Teachers (3 credits)
- MTH 324 - Algebra for Elementary Teachers (3 credits)
- MTH 331 - Euclidean Geometry (3 credits)

**Year Four**

- Capstone course
- Student teaching
- Appropriate courses in general education
- MTH 350 - Modern Algebra I (3 credits)

#### Mathematics Major with Secondary Certification Emphasis

**Year One**

- Appropriate courses in general education
- MTH 201 - Calculus I (4 credits)
- MTH 202 - Calculus II (4 credits)
- MTH 210 - Communicating in Mathematics (4 credits)
- PSY 101 - Introductory Psychology (3 credits)

**Year Two**

- Appropriate courses in general education
- MTH 203 - Calculus III (4 credits)
- MTH 204 - Linear Algebra I (3 credits)
- MTH 229 - Mathematical Activities for Secondary Teachers (3 credits)
- MTH 329 - Teaching Middle Grades Mathematics (3 credits)

**Year Three**

- Elective in the major
- Student assisting
- Cognate course for major
- Appropriate courses in general education
- MTH 315 - Discrete Mathematics (3 credits)
- MTH 331 - Euclidean Geometry (3 credits)
- STA 312 - Probability and Statistics (3 credits)

**Year Four**

- Capstone course
- Student teaching
- Appropriate courses in general education
- MTH 350 - Modern Algebra I (3 credits)