#### Major 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 is strongly urged to consult with the Director of Undergraduate Studies.

It is recommended that students considering majoring in mathematics take Introduction to Proof and Problem Solving (200) following Calculus II and 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 be a math major.

##### A.B. Mathematics Major

The AB degree requires a total of 10 courses.

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

The four core courses, Calculus II (036), Multivariable Calculus (137), Linear Algebra (150), and Introduction to Proof and Problem Solving (200), introduce basic mathematical concepts as well as develop students’ mathematical reasoning and communication skills. Students will further develop abstract reasoning skills in the required upper level courses Abstract Algebra (215) and Analysis I (310).

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. Abstract Algebra is normally taken in the junior year, Analysis I in Fall of senior year. An upper level course may be substituted for Calculus II, Multivariable Calculus, and Linear Algebra for students passing an appropriate departmental placement test.

##### B.S. Mathematics Major

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.

- Calculus II (036) (Prerequisite: Calculus I (035), four credits of Calculus AP credit, or passing a departmental exam)
- Multivariable Calculus (137)
- Linear Algebra (150)
- Introduction to Proof and Problem Solving (200) (Prerequisite: B or better in 036 or department approval)
- Mathematical Statistics (140)
- Abstract Algebra (215)
- Analysis I (310)
- Complex Variables (316)
- 4 Mathematics electives at level of 200 or higher
- Computer Science I (COSC-051) or equivalent

The four core courses, Calculus II (036), Multivariable Calculus (137), Linear Algebra (150), and Introduction to Proof and Problem Solving (200), introduce basic mathematical concepts as well as develop students’ mathematical reasoning and communication skills. Students will further develop abstract reasoning skills in the required upper level courses Abstract Algebra (215) and Analysis I (310).

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. Abstract Algebra is normally taken in the junior year, Analysis I in Fall of senior year. An upper level course may be substituted for Calculus II, Multivariable Calculus, and 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 four 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), Mathematical Logic (PHIL-482), Modeling of Biological Populations (BIOL-422).

#### Minor in Mathematics

The minor requires a minimum of six courses, with five of the courses at the 100 level or above.

- Calculus II (036) (Prerequisite: Calculus I (035), four credits of Calculus AP credit, or passing a departmental exam)
- Multivariable Calculus (137)
- Linear Algebra (150)
- 3 Mathematics electives at level of 140 or higher

An upper level course may be substituted for Calculus II, Multivariable Calculus, and 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.

#### 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 B+ average in mathematics courses to participate and will take an independent study tutorial (MATH-301) during the fall of senior year.

#### 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 (215), and Analysis I (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.

#### 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. A student who scores either 4 or 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). A student who scores 4 or 5 on the Calculus AB examination is awarded four credits for Calculus I (035) and can proceed to Calculus II (036). 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, and 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 sections on Advanced Placement and International Baccalaureate in this *Bulletin *for information about advanced placement in statistics.

(For course listings for Mathematics see http://courses.georgetown.edu)