# Mathematics

The Department of Mathematics and Statistics offers an A.B. in Mathematics, a B.S. in Mathematics, a minor in Mathematics, and a minor in Statistics.

## Majors in Mathematics

The Department of Mathematics and Statistics offers two majors. The A.B. major is designed for students planning graduate study or employment outside mathematics (medicine, law, business, finance, journalism, government service, or pre-college teaching). The B.S. major is designed for students planning graduate study or employment in mathematics. Any student contemplating a math major or minor in math is encouraged to contact the Director of Undergraduate Studies, Prof. Michael Raney, at mwr23@georgetown.edu.

Multivariable Calculus (137), Linear Algebra (150), and Introduction to Proof and Problem Solving (200) may be taken in any order. It is recommended that students considering majoring in mathematics take Introduction to Proof and Problem Solving (200) as soon as possible following Calculus II (036), ideally by no later than fall of their sophomore year. This course gives students a good understanding of what is involved in higher mathematics and will help them decide if they want to pursue a math major.

### Requirements for the A.B. in Mathematics Major

The AB degree requires a total of 10 courses:

- MATH-036 Calculus II (Prerequisite: Calculus I (MATH-035), four credits of Calculus AP credit, or passing a departmental exam)
- MATH-137 Multivariable Calculus
- MATH-150 Linear Algebra
- MATH-200 Introduction to Proof and Problem Solving (Prerequisite: B or better in MATH-036 or department approval)
- MATH-201 Ordinary Differential Equations
- MATH-215 Abstract Algebra
- MATH-310 Analysis I
- 3 Mathematics electives at the 140+ level

Because of the Calculus I prerequisite, students who cannot complete MATH-036, 137, 150, and 200 by the end of their sophomore year should postpone 150 to their junior year. An upper level course may be substituted for Calculus II, Multivariable Calculus, or Linear Algebra for students passing an appropriate departmental placement test.

### Requirements for the B.S. in Mathematics

The BS degree is normally for students interested in graduate studies in a quantitative subject, and as such, students with this major are expected to keep at least a B average in their mathematics courses. This degree requires a total of 13 courses.

- MATH-036 Calculus II (Prerequisite: Calculus I (MATH-035), four credits of Calculus AP credit, or passing a departmental exam)
- MATH-137 Multivariable Calculus
- MATH-140 Introduction to Mathematical Statistics. ANLY-511 may be used as a substitute for MATH-140. Students who have taken ECON-121 should take another Statistics elective at the 200+ level instead of MATH-140.
- MATH-150 Linear Algebra
- MATH-200 Introduction to Proof and Problem Solving (Prerequisite: B or better in 036 or department approval)
- MATH-201 Ordinary Differential Equations
- MATH-215 Abstract Algebra
- MATH-310 Analysis I
- MATH-316 Complex Variables
- 3 Mathematics electives at the 200+ level

Corollary course requirement:

- COSC-051 Computer Science I, or MATH-110 Introduction to Programming for Data Science, or equivalent

Because of the Calculus I prerequisite, students who cannot complete 036, 137, 150, and 200 by the end of their sophomore year should postpone 150 to their junior year. An upper level course may be substituted for Calculus II, Multivariable Calculus, or Linear Algebra for students passing an appropriate departmental placement test.

To encourage the serious math major to see some significant applications of mathematics, one of the three electives for the BS degree can be a mathematically intensive course in another discipline (approved by the Director of Undergraduate Studies), such as Physical Chemistry Lectures (CHEM-219/220), Efficient Computing Methods (COSC-504), Game Theory (ECON-459), Relativity and Quantum Physics (PHYS-153), and Modeling of Biological Populations (BIOL-422).

### Mathematics Honors

A junior majoring in mathematics may apply to perform a research project in the senior year with a mathematics faculty mentor leading to a substantial paper and an oral presentation. A committee of three mathematics faculty members must approve the initial application, and whether to approve the final paper prior to the oral presentation. Normally an applicant should have a A- average in mathematics courses to participate and will take an independent study tutorial (MATH-301) during the fall of senior year. For more information, including how to apply, contact Prof. Michael Raney at mwr23@georgetown.edu.

### Writing in Mathematics

By the time they graduate, mathematics majors should be able to describe reasons for series of calculations, prove mathematical statements at a variety of levels of complexity, and discuss implications and limitations of solutions to problems or methods of proof. The mathematics majors will achieve this writing competence primarily through three required courses: Introduction to Proof and Problem Solving (MATH-200), Abstract Algebra (MATH-215), and Analysis I (MATH-310). In each of these courses, students will complete frequent written assignments, and revise selected assignments. Students will also regularly analyze and critique examples of both student and professional mathematical prose. To meet professional standards of presentation, students will be required to complete some writing assignments using a scientific typesetting environment.

## Minor in Mathematics

### Requirements for the Minor

The minor in mathematics requires the following six courses.

- MATH-036 Calculus II (Prerequisite: Calculus I (035), four credits of Calculus AP credit, or passing a departmental exam)
- MATH-137 Multivariable Calculus
- MATH-150 Linear Algebra
- 3 Mathematics electives at the 140+ level. At least two of these must be non-Statistics electives.

An upper-level course may be substituted for Calculus II, Multivariable Calculus, or Linear Algebra for students passing an appropriate departmental placement test. The math minor must take a minimum of two 200+ level courses within the department, regardless of transfer credit or study abroad credit.

## Minor in Statistics

The Minor in Statistics is designed to develop skills that complement various major degree programs in the social and natural sciences. The program will help students master statistical reasoning, the basics of statistical theory, and advanced techniques in data analysis. The Statistics minor will provide valuable preparation for postgraduate professional and academic degree programs and will broaden the possibilities for employment.

#### Requirements for the Statistics Minor

The minor in statistics requires the following six courses:

- MATH-036 Calculus II
- MATH-105 Data Visualization and Graphics (formerly MATH-225)
- MATH-140 Introduction to Mathematical Statistics. ANLY-511 may be used as a substitute for MATH-140. Students who have taken ECON-121 should take a third Statistics elective at the 200+ level instead of MATH-140.
- MATH-240 Applied Statistical Methods
- Two Statistics electives at the 200+ level (e.g., MATH-245, MATH-325, MATH-340, MATH-345, MATH-426)

Notes:

- Calculus I (MATH-035, or its equivalent in the form of AP/IB credit or passing score on departmental exam) is a prerequisite for Calculus II.
- Subject to approval for content and level of the course, a student may take one of the statistics electives outside of the department.
- A statistics minor must take a minimum of two 200+ level courses within the department, regardless of transfer credit or study abroad.
- Students majoring in Mathematics (A.B. or B.S.) are
**not**eligible to pursue the minor in Statistics.

For more information or to discuss how the minor in statistics can fit your schedule and complement your major field of study, contact Prof. Michael Raney at mwr23@georgetown.edu.

#### Writing in Statistics

Communicating statistical results in a clear and concise written report is an essential part of any data analysis project. In particular, reports need to be written in a way that will be meaningful and informative for non-statisticians. Since the ability to communicate results is central to the study of statistics at any level, writing skills are emphasized starting from the introductory statistics level (in homework assignments) and more substantially in the advanced applied statistics courses where students conduct an actual data analysis project and submit a professional written report.

For more details on the Writing Requirement, see http://mathstat.georgetown.edu/resources/integrated-writing-requirement

## Advanced Placement

Prospective students are encouraged to take an Advanced Placement examination in Mathematics or Statistics. A student who scores a 5 on the Calculus BC examination is awarded eight credits for Calculus I (035) and Calculus II (036) and can proceed to Multivariable Calculus (137), Linear Algebra (150) or Introduction to Proof and Problem Solving (200). A student who scores 5 on the Calculus AB examination, a 4 on the Calculus BC examination, or a 5 on the Calculus AB subscore of the Calculus BC examination is awarded four credits for Calculus I (035) and can proceed to Calculus II (036). A student who scores a 5 on the Statistics examination is awarded four credits for Probability and Statistics (040). Students who do not earn credit by means of an AP examination but who believe that their preparation in high school is substantially equivalent to Calculus I may take a placement examination administered by the Department of Mathematics and Statistics during the registration period at the beginning of the fall term. Passing this exam allows the student to move directly to Calculus II. Additionally, students can petition the department to take a placement exam for Calculus II, Multivariable Calculus, or Linear Algebra. Passing such an exam does not result in credit but allows the math major or minor to replace the course with an upper level mathematics course. Further information may be obtained from the Department of Mathematics and Statistics or from the College Dean’s Office. See the section on Advanced Credit in this *Bulletin *for information about advanced placement in mathematics or statistics.

(For course listings for Mathematics see Schedule of Classes)