# Mathematics (B.S.)

The courses offered by the Department of Mathematics serve several purposes; they supply the mathematical preparation necessary for students specializing in the physical, life or social sciences, in business administration, in engineering, and in education; they provide a route by which students may achieve a level of competence to do research in any of several special mathematical areas; they allow students to prepare themselves for work as mathematicians and statisticians in industry and government; and they give an opportunity to all inquisitive students to learn something about modern mathematical ideas.

### Admission Requirements

Admission requirements for this program are satisfied by the general requirements for undergraduate admission to the University. Undergraduates declaring a mathematics major are strongly encouraged to meet with a departmental advisor before doing so. After a student's acceptance as a major, a student should consult a Departmental advisor at least once a semester to verify progress.

Candidates must complete 120 credits in course work including satisfaction of the University General Education Requirements and the College of Liberal Arts and Sciences Group Requirements, as well as the departmental major requirements cited below. All course work must be completed in accordance with the regulations of the University and the College governing undergraduate scholarship and degrees. The cumulative grade point average in mathematics (MAT) and statistics (STA) courses required for completion of a major option must be at least 2.0 and all coursework required must have a C- or better grade. A minimum of 15 credits of required coursework for the major at the 5030 level or above must be taken at Wayne State.

## SPECIAL PROGRAMS

## Emerging Scholars Program

The Emerging Scholars Program is a special honors program at the levels of MAT 1800, MAT 2010, and MAT 2020, that features collaborative learning through a challenging problem-solving workshop attached to the regular class. Each ESP calculus course (MAT 2010 and MAT 2020) carries four honors credits, though MAT 1800 does not offer honors credits. The program seeks dedicated, hard-working students who want to excel in mathematics. Students who place into the level below MAT 1800 are encouraged to enroll in MAT 1050 PREP as preparation for the Program. Contact the Department for further information.

## ‘AGRADE’ Program (Accelerated Graduate Enrollment)

Our AGRADE Program provides the opportunity for top students to enroll simultaneously in an undergraduate and graduate program. Students can apply a maximum of 16 credits toward both an undergraduate and a graduate degree in the student's major field. Students electing AGRADE programs may expect to complete the bachelor's and master's degrees in five years of full-time study if they take full advantage of the program. For more details about the AGRADE ‘AGRADE’ Program, contact one of the graduate mathematics advisors, or the Graduate Office of the College of Liberal Arts and Sciences (313-577-2516).

## Mathematics Departmental Honors Program

In order to graduate with honors in mathematics, students must satisfy the following criteria:

- Completion of the requirements for a Bachelor of Science degree.
- Have an overall grade point average of 3.3 or above at graduation.
- At least 12 math honors credits at the level of MAT 2020 or above, including at least 4 credits of an approved 5000 level course. See a math advisor for approved courses. MAT 4990 is not included in these 12 credits. The student must complete the course with at least a B and the honors option work with at least a B in order to obtain honors credit.
- Completion of an HON 42XX - Honors College Seminar. See the Honors College website for information.
- Satisfactory completion of MAT 4990 - Directed Study: Honors Program (3-6 credits). MAT 4990 involves the completion of an honors thesis in mathematics. The thesis must extend, supplement or compliment the 5000 level coursework the student has taken. It must be written under the guidance of a full-time faculty member.
- Obtain a 3.3 average for all math classes upon completion.

## Senior Rule

In their last undergraduate semester, Wayne State students with a 3.0 (or above) upper division grade point average have the option of taking a limited number of graduate credits. Graduate credit is awarded only for those courses taken in excess of baccalaureate degree requirements. Undergraduate and graduate courses combined may not exceed sixteen credits for the final semester of baccalaureate degree course work. For more information look under graduate admissions in the graduate bulletin.

## REQUIREMENTS

#### Minimum Grade Requirements

The following grade requirements must be satisfied to obtain the degree.

- C- or better if a course is a prerequisite for another course.
- C or better average grade for all courses.

#### B. S. Additional Requirements

The candidate must complete the following courses in addition to choosing concentration A, B, C, or D as described below.

Code | Title | Credits |
---|---|---|

MAT 5600 | Introduction to Analysis I ^{1} | 4 |

Select one of the following two options: | ||

University Physics for Scientists I and University Physics Laboratory | ||

University Physics for Engineers I and University Physics Laboratory | ||

Select one of the following two options: | ||

University Physics for Scientists II and University Physics Laboratory II | ||

University Physics for Engineers II and University Physics Laboratory II | ||

Select one of the following two options: | 3-4 | |

Problem Solving and Programming and Problem Solving and Programming Laboratory | ||

Introduction to C++ Programming Language | ||

Select one of the following six options: | 3-5 | |

Basic Life Mechanisms | ||

General Chemistry I and General Chemistry I Laboratory | ||

Nutrition and Health and Nutrition Laboratory | ||

Geology: The Science of the Earth and Geology: The Science of the Earth Laboratory (If taken before Winter 2018, GEL 1010 alone will meet the requirement.) | ||

Human Nutrition and Nutrition Laboratory | ||

Introductory Psychology | ||

Total Credits | 10-13 |

^{1} | A candidate for the B. S. degree in mathematics who is pursuing a second major does not have to complete MAT 5600 unless the concentration requires it. A candidate for the B. S. degree in mathematics who is pursuing a second degree must complete the course. |

### Concentrations

The candidate must complete one of the following concentrations in addition to requirements listed above. Note that STA courses previously designated by MAT (for example STA 2210 was previously labelled MAT 2210) are the same courses and meet the same requirements.

#### Concentration A: Prospective Graduate Study

This concentration is recommended for students who plan to pursue graduate study in mathematics.

Code | Title | Credits |
---|---|---|

MAT 2010 | Calculus I | 4 |

MAT 2020 | Calculus II | 4 |

MAT 2030 | Calculus III | 4 |

Select one of the following two options (MAT 2350 is preferred if available, and it is 3 credits rather than 4): | 3-4 | |

Elementary Differential Equations | ||

Differential Equations and Matrix Algebra | ||

MAT 2250 | Elementary Linear Algebra | 3 |

MAT 5070 | Elementary Analysis | 4 |

MAT 5420 & MAT 5993 | Algebra I and Writing Intensive Course in Mathematics | 4 |

MAT 5600 | Introduction to Analysis I | 4 |

MAT 5700 | Introduction to Probability Theory | 4 |

Select one of the following two options: | 3-4 | |

Algebra II | ||

Introduction to Analysis II | ||

Select one of the following six options: | 3-4 | |

Complex Variables and Applications | ||

Algebra II | ||

Introduction to Topology | ||

Elementary Differential Geometry and its Applications | ||

Introduction to Analysis II | ||

Introduction to Mathematical Statistics | ||

Select one of the following four options: | 3-4 | |

An MAT or STA course numbered 5030 or above ^{1} | ||

Theory of Languages and Automata | ||

Matrix Computation I | ||

Topics in Computer Science (The topic must be approved by the Math Department Undergraduate Committee.) | ||

Total Credits | 43-47 |

^{1} | Excluding MAT 5120, MAT 5130, MAT 5180, MAT 5190, MAT 5992, MAT 6130, MAT 6150, MAT 6170, MAT 6180, MAT 6200, or MAT 6210. Only one (at most) of the courses may be selected from MAT 5890 or MAT 5990. These electives are subject to advisor approval on the Student's Plan of Work. |

#### Concentration B: General Topics

This concentration is for students interested in a broad range of topics.

Code | Title | Credits |
---|---|---|

MAT 2010 | Calculus I | 4 |

MAT 2020 | Calculus II | 4 |

MAT 2030 | Calculus III | 4 |

Select one of the following two options (MAT 2350 is preferred if available, and it is 3 credits rather than 4): | 3-4 | |

Elementary Differential Equations | ||

Differential Equations and Matrix Algebra | ||

MAT 2250 | Elementary Linear Algebra | 3 |

MAT 5070 | Elementary Analysis | 4 |

MAT 5700 | Introduction to Probability Theory | 4 |

MAT 5420 & MAT 5993 | Algebra I and Writing Intensive Course in Mathematics | 4 |

Select one of the following: ^{1} | 9-12 | |

Three additional MAT or STA courses numbered 5030 or above ^{1} | ||

OR | ||

Two such courses, plus one of the following: (depending on topic) | ||

Theory of Languages and Automata | ||

Design and Analysis of Algorithms | ||

Matrix Computation I | ||

Topics in Computer Science (depending on the topic) | ||

Total Credits | 39-43 |

^{1} | Excluding MAT 5120, MAT 5130, MAT 5180, MAT 5190, MAT 5992, MAT 6130, MAT 6150, MAT 6170, MAT 6180, MAT 6200, or MAT 6210. Only one (at most) of the courses may be selected from MAT 5890 or MAT 5990. These electives are subject to advisor approval on the Student's Plan of Work. |

#### Concentration C: Secondary Teaching

This concentration is designed for students who would like to be qualified to be secondary school teachers. Although certification for secondary teaching can be combined with any other concentration, **this concentration is available only to students who complete secondary teacher certification prior to graduation.**

Code | Title | Credits |
---|---|---|

MAT 2010 | Calculus I | 4 |

MAT 2020 | Calculus II | 4 |

MAT 2030 | Calculus III | 4 |

MAT 2250 | Elementary Linear Algebra | 3 |

STA 2210/MAT 6150 | Probability and Statistics | 4 |

MAT 2860/6130 | Discrete Mathematics | 3 |

MAT 5000 | Fundamental Concepts of Mathematics and Proof Writing | 3 |

MAT 5070 | Elementary Analysis | 4 |

MAT 6140 | Geometry: An Axiomatic Approach | 3 |

MAT/MAE 6200 | Teaching Arithmetic, Algebra and Functions from an Advanced Perspective | 3 |

Select one of the following two options (MAT 5420 is preferred): | 4 | |

Algebra I and Writing Intensive Course in Mathematics | ||

Algebra: Ring Theory Through Exploration, Conjecture, and Proof and Writing Intensive Course in Mathematics (OR) | ||

Select one of the following four options: | 3-4 | |

Elementary Theory of Numbers | ||

Introduction to Topology | ||

Introduction to Analysis I | ||

Algebra: Group Theory Through Exploration, Conjecture, and Proof | ||

Total Credits | 42-43 |

#### Concentration D: Computer Science

Mathematics and computer science are so closely related that a great many students who major in mathematics pursue careers or graduate study in computer science. A mathematics degree, being more than just welcome in the field, is highly regarded. For students who would like to complete a double degree in mathematics and computer science or a major in mathematics with a minor in computer science, the Department offers a specially designed program. Under this concentration, students can take certain courses that satisfy both mathematics and computer science requirements simultaneously. Specifically, any two of STA 5030, MAT 5100, MAT 5110 or MAT 5890 (The topic for MAT 5890 must be approved by the Department of Computer Science.) can be used as computer science electives, and one of CSC 5860, CSC 5870, CSC 6500, CSC 6620 or CSC 6991 can be used as a mathematics elective (The topic for CSC 6991 must be approved by the Department of Mathematics).

*This concentration is available only to students who complete a second degree or a minor in computer science prior to graduation*. Students should consult the Computer Science Department concerning the requirements for the second degree or minor.

Code | Title | Credits |
---|---|---|

MAT 2010 | Calculus I | 4 |

MAT 2020 | Calculus II | 4 |

MAT 2030 | Calculus III | 4 |

MAT 2250 | Elementary Linear Algebra | 3 |

Select one of the following three options (STA 2210 should not be chosen if the student is doing a second degree in Computer Science, but may be chosen if the student is doing a minor in Computer Science): | 3-4 | |

Introduction to Probability Theory | ||

Probability and Statistics | ||

Basic Engineering III: Probability and Statistics in Engineering | ||

MAT 2860 | Discrete Mathematics | 3 |

MAT 5070 | Elementary Analysis | 4 |

MAT 5100 | Numerical Methods I | 3 |

MAT 5420 & MAT 5993 | Algebra I and Writing Intensive Course in Mathematics | 4 |

Select one of the following: | 6-8 | |

Two additional MAT or STA courses numbered above 5030 ^{2} | ||

OR | ||

One such course from the above, plus one of the following five options: | ||

Introduction to Pattern Recognition and Document Analysis | ||

Computer Graphics I | ||

Theory of Languages and Automata | ||

Matrix Computation I | ||

Topics in Computer Science (Topic must be approved by the Math Department Undergraduate Committee.) | ||

Total Credits | 38-41 |

^{1} | Required for the B.S. degree for students completing a minor in computer science. It is not required for students completing a double degree in mathematics and computer science. |

^{2} | Excluding MAT 5120, MAT 5130, MAT 5180, MAT 5190, MAT 5992, MAT 6130, MAT 6150, MAT 6170, MAT 6180, MAT 6200, or MAT 6210. Only one (at most) of the courses may be selected from MAT 5890 or MAT 5990. These electives are subject to advisor approval on the Student's Plan of Work. |