# 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) courses required for completion of a major option must be at least 2.0.

## Major Requirements

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

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

MAT 5420 & MAT 5993 | Algebra I and Writing Intensive Course in Mathematics (concurrently) ^{1} | 4 |

MAT 5600 | Introduction to Analysis I ^{2} | 4 |

PHY 2170 & PHY 2171 | University Physics for Scientists I and University Physics Laboratory | 5 |

PHY 2180 & PHY 2181 | University Physics for Scientists II and University Physics Laboratory II | 5 |

CSC 1100 & CSC 1101 | Problem Solving and Programming and Problem Solving and Programming Laboratory | 4 |

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

Basic Life Mechanisms | ||

General Chemistry I and General Chemistry I Laboratory | ||

Nutrition and Health and Nutrition Laboratory | ||

GEL 1010 & GEL 1011 | Geology: The Science of the Earth and Geology: The Science of the Earth Laboratory | 4 |

Human Nutrition and Nutrition Laboratory | ||

Introductory Psychology | ||

Total Credits | 29-31 |

^{1} | |

^{2} | A candidate for the B. S. degree who has a second major does not have to complete MAT 5600 unless the concentration requires it. |

### Option A: Prospective Graduate Study

This option 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 |

MAT 2150 | Differential Equations and Matrix Algebra | 4 |

or MAT 2350 | Elementary Differential Equations | |

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 5430 | Algebra II | 3-4 |

or MAT 5610 | Introduction to Analysis II | |

MAT 5700 | Introduction to Probability Theory | 4 |

Select one of the following: | 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 course from one of the following groups: | 1-4 | |

Group A | ||

Any Mathematics course numbered above 5030 ^{1} | ||

Group B | ||

Select one CSC of the following (depending on topic): | ||

Theory of Languages and Automata | ||

Matrix Computation I | ||

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

Total Credits | 38-43 |

^{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. |

### Option B: General Mathematics

This option 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 |

MAT 2150 | Differential Equations and Matrix Algebra | 4 |

or MAT 2350 | Elementary Differential Equations | |

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 5700 | Introduction to Probability Theory | 4 |

Select one of the following: | 9-12 | |

Three additional Mathematics courses numbered 5030 or above OR ^{1} | ||

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 | 40-43 |

^{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. |

### Option C: Secondary Teaching

This option is recommended for students in the Combined Curriculum for Secondary Teaching.

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

MAT 2010 | Calculus I | 4 |

MAT 2020 | Calculus II | 4 |

MAT 2030 | Calculus III | 4 |

MAT 2210/6150 | Probability and Statistics | 4 |

MAT 2250 | Elementary Linear Algebra | 3 |

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 options: | ||

MAT 6170 | Algebra: Ring Theory Through Exploration, Conjecture, and Proof (OR) | 4 |

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

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

Elementary Theory of Numbers | ||

Introduction to Topology | ||

Introduction to Analysis I | ||

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

Total Credits | 46-47 |

### Option 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 major 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 option, students can take certain courses that satisfy both mathematics and computer science requirements simultaneously. Specifically, MAT 5100 can be used as a computer science elective and one of CSC 5860, CSC 5870, CSC 6500, CSC 6620, or CSC 6991 (depending on the topic) can be used as a mathematics elective.

*This option is available only to students who complete a second major or a minor in computer science*. Students should consult the Computer Science Department for their major and minor requirements.

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

MAT 2010 | Calculus I | 4 |

MAT 2020 | Calculus II | 4 |

MAT 2030 | Calculus III | 4 |

MAT 2210/6150 | Probability and Statistics | 4 |

MAT 2250 | Elementary Linear Algebra | 3 |

MAT 2860/6130 | 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 |

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

Select one of the following: | 9-12 | |

Two additional Mathematics courses numbered above 5030 ^{2} | ||

One such course from the above, plus one of the following (depending on topic): | ||

Introduction to Pattern Recognition and Document Analysis | ||

Computer Graphics I | ||

Theory of Languages and Automata | ||

Matrix Computation I | ||

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

Total Credits | 46-49 |

^{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. |

## Mathematics 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.
- 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.
- Completion of a 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.

## Combined Curriculum for Secondary Teaching (CCST)

Under the Combined Curriculum, it is possible to earn a bachelor’s degree in mathematics concurrent with a secondary teaching certificate. Students in CCST may satisfy the mathematics part of their degree requirements by any of the degree options specified below, though Option C is specifically designed and recommended for future teachers. It is recommended but not required that CCST students who do not choose Option C take MAT 2860, MAT 5000, and MAT 6140.

## 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)

The Department of Mathematics participates in the College ‘AGRADE’ (Accelerated Graduate Enrollment) Program, in which qualified students can earn a master’s degree and bachelor’s degree. For more details about the ‘AGRADE’ Program, contact one of the graduate mathematics advisors, or the Graduate Office of the College (313-577-2960).