# 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.

Introduction to Mathematical Statistics (MATH-2140), Linear Algebra (MATH-2250), Multivariable Calculus (MATH-2370), and Introduction to Proof and Problem Solving (MATH-2800) may be taken in any order. It is recommended that students considering majoring in mathematics take Introduction to Proof and Problem Solving (MATH-2800) as soon as possible following Calculus II (MATH-1360), ideally by no later than the 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-1360 Calculus II (Prerequisite: Calculus I (MATH-1350), four credits of Calculus AP/IB credit, or passing a departmental exam)
- MATH-2250 Linear Algebra
- MATH-2370 Multivariable Calculus
- MATH-2410 Ordinary Differential Equations
- MATH-2800 Introduction to Proof and Problem Solving
- MATH-3210 Abstract Algebra
- MATH-3310 Analysis I
- 3 Mathematics electives at the 2000+ level

An upper level course may be substituted for Calculus II, Multivariable Calculus, or Linear Algebra for students passing the corresponding departmental waiver exam.

### 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-1360 Calculus II (Prerequisite: Calculus I (MATH-1350), four credits of Calculus AP/IB credit, or passing a departmental exam)
- MATH-2140 Introduction to Mathematical Statistics. DSAN-5100 may be used as a substitute for MATH-2140. Students who have taken ECON-2110 should take another Statistics elective at the 2000+ level instead of MATH-2140.
- MATH-2250 Linear Algebra
- MATH-2370 Multivariable Calculus
- MATH-2410 Ordinary Differential Equations
- MATH-2800 Introduction to Proof and Problem Solving
- MATH-3210 Abstract Algebra
- MATH-3310 Analysis I
- MATH-4320 Complex Variables
- 3 Mathematics electives at the 2000+ level

Corollary course requirement:

- COSC-1010 Introduction to Computer Science: Python, or COSC-1020 Computer Science I, or MATH-1510 Introduction to Programming for Data Science, or equivalent.

An upper level course may be substituted for Calculus II, Multivariable Calculus, or Linear Algebra for students passing the corresponding departmental waiver exam.

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 Game Theory (ECON-4059), Data Analysis (ECON-4495), Relativity and Quantum Physics (PHYS-2103), Modeling of Biological Populations (BIOL-4220), and Symbolic Logic (PHIL-4000).

### 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 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-2800), Abstract Algebra (MATH-3210), and Analysis I (MATH-3310). 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-1360 Calculus II (Prerequisite: Calculus I (MATH-1350), four credits of Calculus AP/IB credit, or passing a departmental exam)
- MATH-2250 Linear Algebra
- MATH-2370 Multivariable Calculus
- 3 Mathematics electives at the 2000+ level. At least two of these must be non-Statistics electives. MATH-2140 (Introduction to Mathematical Statistics) may be regarded as a Mathematics elective for this purpose.

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 2000+ level electives 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-1505 Data Visualization and Graphics
- MATH-2140 Introduction to Mathematical Statistics. DSAN-5100 may be used as a substitute for MATH-2140. Students who have taken ECON-2110 should take another Statistics elective at the 2000+ level instead of MATH-2140.
- MATH-2540 Regression Analysis. PSYC-5004 may be used as a substitute for MATH-2540. A student who has taken PSYC-5004 and is applying it to a Psychology major or another major must take another 2000+ Statistics elective in place of MATH-2540.
- Two Statistics electives at the 2000+ level (e.g., MATH-2620 Statistical Learning and Data Science, MATH-2625 Biostatistics, MATH-2640 Advanced Regression Methods, MATH-2645 Applied Time Series)

Subject to approval for content and level of the course, a student may take one of the StatisticsÂ electives outside of the department. One such course is ECON-5554 Data Analysis.

A Statistics minor must take a minimum of three 2000+ level Statistics 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 (MATH-1350) and Calculus II (MATH-1360) and can proceed to Linear Algebra (MATH-2250), Multivariable Calculus (MATH-2370), or Introduction to Proof and Problem Solving (MATH-2800). 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 (MATH-1350) and can proceed to Calculus II (MATH-1360). A student who scores a 5 on the Statistics examination is awarded four credits for Probability and Statistics (MATH-1040). 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)

**Calculus Readiness Assessment**

Students planning to enroll in a **first course in Calculus **must first take a **Calculus Readiness Assessment**. This assessment measures studentsâ€™ knowledge of concepts from **Basic Math through Precalculus**. Students must earn a **minimum score of 75** to enroll in the standard one-semester Calculus I (MATH-1350) course. Students who earn **a score between 40 and 74** must register in the one-year sequence of Calculus with Review A (MATH-1310) and Calculus with Review B (MATH-1320), which cover the same concepts at a slower pace, incorporating Algebra and Precalculus reviews as needed. MATH-1310 does not satisfy the general education requirement in mathematics and is counted as a free elective. Students will get math credit only after completion of MATH-1320. They will then be able to move on to other courses that have Calculus I as a prerequisite.

The Calculus Readiness Assessment must be taken before enrolling in either MATH-1310 or MATH-1350. Once students have enrolled in MATH-1310, they must take the sequence MATH-1310/MATH-1320 and cannot switch to MATH-1350. In particular, a student who has enrolled in MATH-1310 cannot retake the Calculus Readiness Assessment in order to switch into MATH-1350.

The Calculus Readiness Assessment consists of up to **30 questions and must be completed in one 2-hour sitting**. It is an **open-response assessment** (not multiple choice) that requires students to work out solutions to be entered into the system. Once an answer is submitted, it cannot be changed, so be sure to check your answer carefully before submitting it. No outside resources can be consulted for help. An **on-screen calculator is provided **if one is needed to complete a particular problem. Otherwise, the use of a calculator is not allowed.

Students can attempt the Calculus Readiness Assessment up to **three times**. If students do not obtain a score of at least 75 on the first attempt, they must spend at least 5 hours working through the individualized Prep and Learning Modules and wait at least 48 hours before their second attempt. The same applies between the second and third attempt.

Click the link below to start the Calculus Readiness Assessment. **A valid Georgetown NetID and password are needed to start the assessment**:

https://secure.aleks.com/shiblogon/sso?sso_account=fabf73e&class_code=HRN6H-PTYN3 (new window) (new window)

**Departmental Waiver Exams**

Students who believe their preparation in high school is substantially equivalent to Calculus I (MATH-1350), Calculus II (MATH-1360), Linear Algebra (MATH-2250), or Multivariable Calculus (MATH-2370) may place out of these courses by taking the corresponding departmental Waiver Exam in the individual subject. **Students who pass a Waiver Exam will receive a course waiver and may register for more advanced courses**. However, course credit is not awarded for passing any Waiver Exam.

Each Waiver Exam is a handwritten two-hour exam. No calculator is allowed on any Waiver Exam.

Students interested in taking a Waiver Exam should inform Professor Michael Raney of which Waiver Exam (Calculus I, Calculus II, Liner Algebra, or Multivariable Calculus) they intend to take. The Waiver Exams are typically administered during New Student Orientation in the run-up to the fall semester.