**General Information**

Students who have special placement problems, or are unclear about their level, should make an appointment with a faculty member or the chair.

Two help rooms, one in 406 Mathematics and one in 333 Milbank, will be open all term for students seeking individual help and counseling from the instructors and teaching assistants. No appointments are necessary. However, resources are limited and students who seek individual attention should make every effort to come during the less popular hours and to avoid the periods just before midterm and final exams.

**Courses for First-Year Students**

The systematic study of Mathematics begins with one of the following alternative sequences: Calculus I, II, III, IV (Math V 1101--2, V 1201--2); Honors Math A--B (Math V 1207--8).

Credit is allowed for only one of the calculus sequences. The calculus sequence is a standard course in differential and integral calculus. Honors Mathematics A--B is for exceptionally well-qualified students who have strong advanced placement scores. It covers second-year Calculus (Math V 1201--2) and Linear Algebra (Math V 2010), with an emphasis on theory.

Calculus II is NOT a prerequisite for Calculus III, so students who plan to take only one year of calculus may choose between I and II or I and III. The latter requires a B or better in Calculus I and is a recommended option for some majors.

Introduction to Higher Mathematics (MATH V 2000) is a course that can be taken in their first or second year by students with an aptitude for mathematics who would like to practice writing and understanding mathematical proofs.

**Placement in the Calculus Sequence**

College Algebra and Analytical Geometry: A refresher course for students who intend to take Calculus but do not have adequate background for it.

Advanced Placement: Students who have passed the advanced placement test for Calculus AB with a grade of 4 or 5 or BC with a grade of 4 receive 3 points of credit. Those who passed Calculus BC with a grade of 5 will receive 4 points of creditor 6 points on placing into Calculus III or Honors Math A and completing with a grade of C or better.

Calculus I, II, III: Students who have not previously studied calculus should begin with Calculus I. Students with 4 or higher on the Calculus AB or BC advanced placement test may start with Calculus II. Students with 5 on the Calculus BC test should start with Calculus III.

Honors Mathematics A: Students who have passed the Calculus BC advanced placement test with a grade of 5, and who have strong mathematical talent and motivation, should start with Honors Mathematics A. This is the most attractive course available to well-prepared, mathematically talented first-year students, whether or not they intend to be mathematics majors. Students who contemplate taking this course should consult with the instructor. If this is not possible ahead of time, they should register and attend the first class.

Read about math beyond calculus

**Requirements for the Major**

The majors program in both mathematics and applied mathematics are appropriate for students who plan to continue their training in graduate school. Students who begin with Honors Mathematics A--B will need to plan their succeeding course carefully with the help of an adviser.

### For a major in Mathematics

14 courses as follows:

**Four courses **in calculus or Honors Mathematics A--B, including Advanced Placement Credit.

**Six courses** in mathematics numbered at or above 2000

**Four courses** in any combination of mathematics and cognate courses.

The courses in mathematics **must include**:

V 2010 | Linear Algebra |

(or Honors Mathematics A--B) | |

W 4041--2 | Introduction to Modern Algebra* |

W 4061--2 | Introduction to Modern Analysis* |

V 3951x, 3952y | Undergraduate Seminar in Mathematics (at least one term) |

However, students who are not contemplating graduate study in mathematics may replace one or both of the two terms of MATH W 4061--W 4062 by one or two of the following courses: MATH V 2500, V 3007, or W 4032. In exceptional cases, the chair will approve the substitution of certain more advanced courses for those mentioned above.

*Note: It is strongly recommended that the sequences Math W 4041--2 and W 4061--2 be taken in separate years.

### For a major in Applied Mathematics:

**14 courses** plus **Junior Seminar in Applied Mathematic**

**Four courses** in Calculus or Honors Mathematics A--B, including Advanced Placement Credit.

V 2010 | Linear Algebra |

W 4061 | Introduction to Modern Analysis |

APMA E 4901 | Seminar in Applied Mathematics: Fall, junior year |

APMA E 4903 | Seminar in Applied Mathematics: Fall, senior year |

APMA E 3900 | Undergraduate Research in Applied Mathematics |

(APMA E 3900 be replaced by the combination APMA E 4902/4904, second semester of the junior and senior applied mathematics seminar, when these are offered or, with approval, another technical elective for seniors that involves an undergraduate thesis or creative research report.)

Additional electives, to be approved by the Applied Math Committee, e.g.:

V 2500 | Analysis and Optimization |

V 3007 | Complex Variables |

V 3027 | Ordinary Differential Equations |

V 3028 | Partial Differential Equations |

V 3030 | Dynamical Systems |

W 4032 | Fourier Analysis |

SIEO W 3658 | Probability |

APMA E4300 | Numerical Methods |

### For a major in Mathematics-Statistics:

14 courses:

**Five courses** in mathematics:

V 1101, V 1102 and V 1201 | Calculus I, II and III or equivalent |

MATH V 2010 | Linear Algebra |

MATH V 2500 | Analysis and Optimization |

**Five courses** in statistics:

STAT W 1211 | Introduction to Statistics B |

STAT W 3000 | Introduction to Statistics: Probability Models or SIEO W 4105 Probability |

STAT W 3659 or W 4107 | Statistical Inference |

STAT W 4315 | Linear Regression Models |

IEOR E 4106 | Introduction to Operations Research: Stochastic processes |

**One course** in computer science that requires substantial work in programming.

**Three courses** of electives: An approved selection of advanced courses in mathematics, statistics, applied mathematics, computer science, or mathematical methods courses in physical or social sciences, including biology, economics, and physics.

Students should plan to include **a senior thesis** or **the Undergraduate Seminar in Mathematics** in their program, in consultation with their advisors.

Note: Students must obtain approval from an adviser in each of the two departments before selecting electives. Students should take MATH V 2010 Linear Algebra in the second semester of the second year. With the approval of their adviser, students may replace the two requirements STAT W 3000 or SIEO W 4105 and STAT W 3659/4107 with the 6-point course STAT W 4109.

### For a major in Mathematics--Computer Science:

15 courses as follows:

Courses in mathematics:

V 1101, V 1102, V 1201, V 1202 | Calculus I, II, III, IV (including AP Credit) |

or V 1207, V 1208 | Honors Math A, B (Note A) |

V 2010 | Linear Algebra |

V 3020* | Number Theory and Cryptography (Note B) |

W 4041 | Introduction to Modern Algebra |

W 4061* | Introduction to Modern Analysis (Note C) |

V 3951 or V 3952 | Undergraduate Seminars in Mathematics |

Courses in computer science:

W 1004 |
Computer Science I (or AP credit) |

W1007 | Computer Science II |

W 3137 | Data Structures and Algorithms |

W 3157 | Computer Science III (Advanced Programming) |

W 3203 | Discrete Mathematics |

W 3261 | Computability and Models of Computation |

W 3827 | Fundamentals of Computer Systems |

W 4231* | Analysis of Algorithms I |

W 4241* | Numerical Algorithms and Complexity I |

*Electives--take two of four; in exceptional cases, other courses may be substituted with the approval of departmental representatives of both departments.

Note A: The Honors sequence also fulfills the MATH V 2010 Linear Algebra requirement.

Note B: May substitute MATH V 3021 or BC 2006 or MATH V 1103.

Note C: May substitute MATH V 2500, V 3007, V 4032, V 3386, or W 4051.

Students seeking to pursue a Ph.D. program in either discipline are urged to take additional courses, in consultation with their advisers.

### For a major in Economics and Mathematics

## Requirements for the Minor

### For a minor in Mathematics or Applied Mathematics:

**Six courses** from any of the courses offered by the department except Math W 1003 College Algebra and Analytic Geometry, Math V 1101/2 Calculus I/II.