# Mathematical Sciences Major

**General Information**

The primary goals of the Mathematical Sciences curriculum are to offer general training in mathematical reasoning and to develop mastery of mathematical tools needed for a lifelong series of different jobs and continuing education. Much emphasis is placed on the theory of problem-solving and nurturing such abilities as intuition, inductive and deductive reasoning, and model building.

The student is also made aware of the power and elegance of mathematical truth through careful analysis of axiomatic systems and mathematical theories. Throughout the undergraduate program students are encouraged to formulate their own problems and conjectures, thus challenging their own ability to cope with the mathematical literature.

In fostering these goals the Mathematical Sciences curriculum provides grounding in the traditional areas of theoretical mathematics. It also allows student the flexibility of choosing elective courses based on future career or graduate school goals: pure mathematics, applied mathematics, probability and statistics, or teacher preparation.

In seminars, independent study courses, and internships the student is encouraged to formulate and carry out research projects, working creatively with the literature in either pure, applied mathematics or mathematics education. In the senior year students work individually with a faculty member on their self-selected senior project, which culminates in a research paper and a presentation, usually at the Hudson River Undergraduate Mathematics Conference.

The programs lead to a Bachelor of Science degree in the Mathematical Sciences, including if pursuing the teacher preparation-secondary school major, or a Bachelor of Arts degree in Mathematics, if pursuing the teacher preparation-elementary major. The programs have been patterned to follow the recommendations of the Committee on Undergraduate Programming in Mathematics of the Mathematical Association of America.

Program Objectives

The Mathematical Sciences curriculum provides instruction and support for students in achieving the following objectives. It is our purpose that our students:

1) Learn mathematical habits of mind

a. Correctly apply inductive and deductive reasoning skills.

b. Demonstrate correct use of formal mathematical language and ability to compose a mathematical proof.

c. Demonstrate the ability to successfully apply mathematical computations and algorithms.

d. Demonstrate the ability to do mathematical work independently, and to go beyond the content level of standard coursework.

2) Demonstrate fluency in mathematical communication.

a. Write about mathematics correctly and in a clear manner.

b. Communicate mathematics orally in a clear manner.

3) Use technology relevant to mathematics.

a. Use technology to solve mathematical problems.

b. Use technology to communicate mathematics effectively.

**Career Opportunities**

Graduates in mathematics develop the type of creative thinking and problem-solving abilities required of professional mathematicians. As a consequence, they are well prepared to complete advanced study or pursue a wide variety of employment opportunities in industry, commerce, or the public sector. Graduates have secured positions in the areas of actuarial science, finance, operations research, computer programming, statistics, systems analysis, software engineering, and teaching. Others have received fellowships to pursue graduate study in mathematics or related areas.

## Degree Requirements

### Required mathematics and other courses (36 credit hours)

for the Bachelor of Science degree in the Mathematical Sciences:CS 170 | Technology in Mathematics | 3 cr. |

CS 171 | Programming for Mathematics | 4 cr. |

MATH 133 | Calculus I | 4 cr. |

MATH 134 | Calculus II | 4 cr. |

MATH 235 | Calculus III | 3 cr. |

MATH 281 | Foundations of Mathematics I | 3 cr. |

MATH 282 | Foundations of Mathematics II | 3 cr. |

MATH 306 | Linear Algebra | 3 cr. |

MATH 418 | Introduction to Modern Algebra | 3 cr. |

MATH 421 | Real Analysis | 3 cr. |

MATH 451 | Senior Project I | 1 cr. |

MATH 452 | Senior Project II | 2 cr. |

Total Credit Hours: | 36 |

In addition, the student must take 12 credit hours (four courses) of mathematics electives selected from 300- and 400-level MATH courses.

### Teacher Preparation-Secondary School

If pursuing the Teacher Preparation-Secondary School major, 12 additional credit hours as follows:MATH 121 | Introductory Probability and Statistics | 3 cr. |

or | ||

MATH 120 | Intro Statistics for the Arts & Sciences | 3 cr. |

MATH 371 | Modern Aspects of Geometry | 3 cr. |

MATH 375 | Creative Problem Solving | 3 cr. |

MATH 377 | Elementary Number Theory | 3 cr. |

Total Credit Hours: | 12 |

### To satisfy the science core requirements

Either BIO 107, BIO 108 with BIO 117, BIO 118, CHEM 105, CHEM 106, or PHYS 133, PHYS 134 must be taken to satisfy the science core requirements. PHYS 133, PHYS 134 is recommended. If the BIO or CHEM sequence is taken, then one unit of high school chemistry is required.BIO 107 | General Biology I | 3 cr. |

BIO 108 | General Biology II | 3 cr. |

with | ||

BIO 117 | General Biology Laboratory I | 1 cr. |

BIO 118 | General Biology Laboratory II | 1 cr. |

or | ||

CHEM 105 | General Chemistry I | 4 cr. |

CHEM 106 | General Chemistry II | 4 cr. |

or | ||

PHYS 133 | Mechanics | 4 cr. |

PHYS 134 | Electricity and Magnetism | 4 cr. |

Total Credit Hours: | 8 |

### Teacher Preparation - Elementary School (40 credits)

Required mathematics and other courses for the Bachelor of Arts degree in Mathematical Sciences.

CS 170 | Technology in Mathematics | 3 cr. |

MATH 107 | Mathematics For Elementary Education I | 3 cr. |

MATH 108 | Mathematics for Elementary Education II | 3 cr. |

MATH 120 | Intro Statistics for the Arts & Sciences | 3 cr. |

or | ||

MATH 121 | Introductory Probability and Statistics | 3 cr. |

MATH 133 | Calculus I | 4 cr. |

MATH 134 | Calculus II | 4 cr. |

MATH 235 | Calculus III | 3 cr. |

MATH 281 | Foundations of Mathematics I | 3 cr. |

MATH 282 | Foundations of Mathematics II | 3 cr. |

MATH 306 | Linear Algebra | 3 cr. |

MATH 371 | Modern Aspects of Geometry | 3 cr. |

MATH 377 | Elementary Number Theory | 3 cr. |

MATH 451 | Senior Project I | 1 cr. |

MATH 452 | Senior Project II | 2 cr. |

Total Credit Hours: | 40 |

Note: Concurrent completion of the Elementary Education major, which yields a Bachelor of Arts Degree in Elementary Education, is required for the Teacher Preparation - Elementary School major.

The typical course schedule for the Bachelor of Science degree in the Mathematical Sciences would be constructed from what follows.