# Degree Requirements

2020 - 2021

## Departmental Guidelines

Mathematics is an essential part of a liberal arts education with numerous connections to a variety of disciplines. The study of mathematics is a challenging and exciting activity that sharpens logical reasoning skills and improves problem solving ability. The curriculum is designed so students can apply these skills to analyze both real-world questions and explore sophisticated mathematical theory.

Students interested in the Mathematics major should take:

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

MATH 135 & MATH 145 | Single Variable Calculus and Multi-variable Calculus |

followed by | |

MATH 213 & MATH 300 | Linear Algebra and Differential Equations and Introduction to Proofs |

by end of their sophomore year. |

It is strongly recommended that Mathematics students take:

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

CS 109 | Discovering Computer Science | |

CS 110 | Discovering Computer Science: Digital Media and Games | |

CS 111 | Discovering Computer Science: Scientific Data and Dynamics | |

or CS 112 | Discovering Computer Science: Markets, Polls, and Social Networks | |

by the end of their sophomore year. |

Most upper level mathematics electives fall into two categories: Foundations and Modeling.

Foundation courses focus on teaching abstract reasoning and the reading, creation, and writing of rigorous proofs in the study of the foundational structures of mathematics. Currently these courses are:

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

MATH 400 | Combinatorics |

MATH 410 | Abstract Algebra |

MATH 413 | Advanced Linear Algebra |

MATH 440 | Advanced Analysis |

MATH 445 | Topology |

MATH 447 | Vector Calculus and Complex Analysis |

Modeling courses, while not devoid of proofs, include a significant study of how mathematical techniques can be used to model and analyze real world problems. Currently modeling courses include:

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

MATH 415 | Operations Research |

MATH 425 | Applied Probability |

MATH 427 | Probability Computing and Graph Theory |

MATH 430 | Fourier Analysis |

MATH 435 | Mathematical Modeling |

Other courses, such as:

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

MATH 361 | Directed Study |

MATH 362 | Directed Study |

MATH 363 | Independent Study |

MATH 364 | Independent Study |

include various additional topics. |

Non-major/minor students interested in taking a mathematics course should consider:

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

MATH 115 | Mathematical Methods for the Physical and Social Sciences | |

or MATH 120 | Elements of Statistics |

Students who did not receive a 4 or 5 on the Calculus AB Advanced Placement exam will usually take MATH 135 before MATH 145.

## Mathematics Majors

The CORE courses consist of:

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

MATH 145 | Multi-variable Calculus | |

MATH 213 | Linear Algebra and Differential Equations | |

MATH 220 | Applied Statistics | |

MATH 300 | Introduction to Proofs | |

MATH 395 | Technical Communication I | |

CS 109 | Discovering Computer Science | |

or CS 110 | Discovering Computer Science: Digital Media and Games | |

or CS 111 | Discovering Computer Science: Scientific Data and Dynamics | |

or CS 112 | Discovering Computer Science: Markets, Polls, and Social Networks |

The FOUNDATION courses consist of:

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

MATH 400 | Combinatorics |

MATH 410 | Abstract Algebra |

MATH 413 | Advanced Linear Algebra |

MATH 440 | Advanced Analysis |

MATH 445 | Topology |

MATH 447 | Vector Calculus and Complex Analysis |

MATH 334 | Theory of Computation |

The MODELING courses consist of:

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

MATH 415 | Operations Research |

MATH 425 | Applied Probability |

MATH 427 | Probability Computing and Graph Theory |

MATH 430 | Fourier Analysis |

MATH 435 | Mathematical Modeling |

### Bachelor of Arts Degree

The minimum requirement for the Bachelor of Arts in Mathematics are the six CORE courses plus four courses; two modeling courses and two foundations courses.

### Bachelor of Science Degree

The minimum requirement for the Bachelor of Science in Mathematics are:

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

The six CORE courses plus six courses; three of | |

MATH 410 | Abstract Algebra |

MATH 440 | Advanced Analysis |

MATH 445 | Topology |

and | |

MATH 447 | Vector Calculus and Complex Analysis |

plus three other 400-level courses. |

Students majoring in Math or Computer Science may take up to two cross-listed math or computer science courses to count as requirements in the intended major. These cross listed courses typically satisfy electives in the major.

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

Current cross listed courses | |

MATH 334 | Theory of Computation |

MATH 415 | Operations Research |

MATH 427 | Probability Computing and Graph Theory |

are pre-approved for this policy. | |

MATH 220 | Applied Statistics |

is preapproved for the computer science BS major. Other math and computer science courses must be approved by the department prior to enrollment. |

## Mathematics Minor

The minimum requirements for a mathematics minor are:

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

MATH 145 | Multi-variable Calculus |

MATH 213 | Linear Algebra and Differential Equations |

MATH 220 | Applied Statistics |

MATH 300 | Introduction to Proofs |

and one of | |

CS 109 | Discovering Computer Science |

CS 110 | Discovering Computer Science: Digital Media and Games |

CS 111 | Discovering Computer Science: Scientific Data and Dynamics |

CS 112 | Discovering Computer Science: Markets, Polls, and Social Networks |

**Computational Science Concentration**

Computational Science is the field of study concerned with constructing mathematical models and numerical solution techniques, and using computer algorithms and simulation to analyze and solve scientific, social scientific, and engineering problems.

The Computational Science concentration consists of four core courses:

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

MATH 145 | Multi-variable Calculus |

MATH 213 | Linear Algebra and Differential Equations |

CS 173 | Intermediate Computer Science |

and one of | |

CS 109 | Discovering Computer Science |

CS 110 | Discovering Computer Science: Digital Media and Games |

CS 111 | Discovering Computer Science: Scientific Data and Dynamics |

or | |

CS 112 | Discovering Computer Science: Markets, Polls, and Social Networks |

and an additional course at the 200-level or above. |

This additional course, which may be in another department, must have a strong and persistent mathematical modeling or computing component and must be approved in advance by the Mathematics and Computer Science Department. In addition, the student must take a two-semester sequence of courses in a department other than Mathematics and Computer Science. A written plan for completing the concentration must be approved by the Mathematics and Computer Science Department prior to enrollment in the elective course. In particular, the elective course and cognate requirements above must be chosen in consistence with a valid educational plan for the student of Computational Science (as defined above). Any mathematics major who wishes to complete this concentration must choose a computer science course as an elective course. Any computer science major who wished to complete this concentration must choose a mathematics course as an elective course. A double mathematics and computer science major is not eligible for this concentration.

## Additional Points of Interest

### Research at Denison

Denison offers a number of research opportunities, including funding for summer research projects. The Anderson Foundation and the Denison University Research Foundation (DURF) support qualified students conducting summer research. For off-campus research opportunities in Mathematics, see the Oak Ridge Science Semester or various National Science Foundation Research Experience for Undergraduates experiences. Interested students should consult a faculty member as early as possible in the fall semester.

### Off-Campus Study

The department of Mathematics and Computer Science strongly encourages students to globalize their education by completing some portion of their undergraduate education abroad. A majority of Denison students spend a semester abroad during their junior year and many more spend a second summer abroad. Denison offers a wide range of opportunities to study off-campus that are highly relevant to the Denison experience.

Going abroad allows students to enhance their knowledge while experiencing another culture and way of life. Students gain valuable international experience that will benefit future career goals and/or graduate school opportunities. Math and Computer Science majors who are fluent in another language will have special advantages in the job market.

Students may take up to two classes outside the department to transfer towards the major at Denison. Additional courses taken outside Denison may accrue credit hours towards graduation, but will not contribute to requirements in the major. Courses taken outside the university must be **pre-approved** for acceptance towards major requirements. Students should provide the department chair syllabi for the intended courses for department approval. Students may petition the department chair for exceptions to this policy. In particular, transfer students may be eligible to transfer additional courses towards major requirements.

Highlights