# Course Descriptions

You can find the complete Mathematics Department course offerings for the recent and current semesters, and for future semesters as they become available, on the Registrar's Schedule of Classes.

There are three levels of courses:

At the **introductory level**, we offer standard calculus courses (MATH 1231; the pair MATH 1220 and 1221) for students interested in quantitative fields, as well as courses for liberal arts students seeking to meet the G-PAC requirement in quantitative reasoning (MATH 1007, 1009). We offer two courses especially for School of Business students (MATH 1051, 1252); business students who are mathematically inclined may be better served by MATH 1231 (consult the requirements of your intended major).

At the** intermediate level**, we offer two calculus courses (MATH 1232 and 2233) that complete the standard three course sequence in calculus, linear algebra (MATH 2184 and 2185; most prospective mathematics majors should opt for MATH 2185) and an introduction to proofs, problem solving and the basic concepts of abstract mathematics (MATH 2971).

At the** advanced level, **we offer a wide selection of courses for math majors and minors, including abstract algebra, real and complex analysis, topology, logic, set theory, combinatorics, number theory, differential equations, differential geometry, numerical analysis, financial mathematics, and mathematical modeling.

**Mathematics and Politics (MATH 1007):**This course provides an alternative to math courses designed for liberal arts students seeking to meet the general curriculum requirement in quantitative reasoning. It focuses on the mathematics of social choice, apportionment, and decision-making, areas of mathematics not normally taught in high schools. It requires little background in mathematics or political science, but is more rigorous than a typical freshman math course and involves more writing. This course is offered every semester.**Mathematical Ideas (MATH 1009):****Designed with the liberal arts student in mind, this is a course in “mathematical culture,” which introduces students to the methods of analysis, reasoning and deduction by which mathematical facts are derived. The material discussed is not what your high-school mathematics courses may lead you to expect but more an introduction to mathematical fields such as number theory, graph theory, set theory, logic and probability. This course is offered every semester.****Calculus with Precalculus I and II (MATH 1220 and 1221):****Designed for students who wish to take MATH 1231 but find themselves underprepared, this pair of courses covers precisely the same material as MATH 1231 but at a slower pace, incorporating into the treatment a full discussion of ”precalculus,” the mathematical prerequisites necessary for a full understanding of the first calculus course. The text is the same as for MATH 1231. A supplementary book that covers the algebra and trigonometry background is also used.****Single Variable Calculus I (MATH 1231):****Designed for students interested in quantitative fields such as mathematics, engineering, physics, chemistry and economics, this is the first in a three-course sequence in calculus; MATH 1232 and 2233 complete the sequence. MATH 1231 treats differentiation and integration of algebraic and trigonometric functions, with applications. Any student who contemplates a major in the sciences, economics, engineering or medicine would be well advised, if not required, to take this course. This course is offered every semester.****Finite Mathematics for the Social and Management Sciences (MATH 1051) and Calculus for the Social and Management Sciences (MATH 1252):**MATH 1051 covers systems of linear equations, matrices, linear programming, the mathematics of finance and probability theory; MATH 1252 covers differential and integral calculus with applications to the management and social sciences. MATH 1051 is offered in the fall and summer; MATH 1252 is offered in the spring and summer. These courses may be taken in any order.

The standard three course sequence in calculus is completed with:

- MATH 1232: Single Variable Calculus II, and
- MATH 2233: Multivariable Calculus.

MATH 1232 is a continuation of MATH 1231 and it considers calculus of exponential and logarithmic functions, various techniques of integration of single variable functions, and sequences and series. MATH 2233 covers differential, integral and vector calculus of functions of several variables. The text for these courses is the same as for MATH 1231.

**Math majors should also complete the following courses before taking upper-level courses, most of which require some combination of these as prerequisites.**

- MATH 2185: Linear Algebra I for Math Majors (preferred), or MATH 2184: Linear Algebra I (see the Program Requirements)
**MATH 2971: Introduction to Mathematical Reasoning**

Algebra and Number Theory (x1xx):

- 3120: Elementary Number Theory
- 3125: Linear Algebra II
- 4121: Introduction to Abstract Algebra I
- 4122: Introduction to Abstract Algebra II

Analysis (x2xx)

- 3257: Introduction to Complex Variables
- 4239: Real Analysis I
- 4240: Real Analysis II

Applied Mathematics (x3xx):

- 3342: Ordinary Differential Equations
- 3343: Partial Differential Equations
- 3359: Introduction to Mathematical Modeling

Math Applications (x4xx):

- 3410: Mathematics of Finance
- 3411: Stochastic Calculus Methods in Finance

Computation and Numerical Analysis (x5xx):

- 3553: Introduction to Numerical Analysis

Combinatorics and Graph Theory (x6xx):

- 3613: Introduction to Combinatorics
- 3632: Introduction to Graph Theory

Mathematical Logic (x7xx):

- 3710: Introduction to Mathematical Logic
- 3720: Axiomatic Set Theory
- 3730: Computability Theory
- 3740: Computational Complexity

Topology/ Geometry (x8xx):

- 3806: Introduction to Topology
- 3848: Differential Geometry

## Choosing the Right First-Year Courses

Your introductory-level math courses typically depend on two things: the school you are enrolled in and your potential major. The descriptions here provide a rough guide. Also consult the requirements for your potential major in the University Bulletin. If none of the situations described apply to you, consult your academic advisor about your program’s math requirements.

**Course to take:** Calculus.

**Determine which level of calculus to take:**

- If you do not have AP credit for Calculus I, then take the placement test, which will help you find the version of Calculus I that fits your level of preparation.
- MATH 1231 is the typical starting place for students who have not received AP credit for calculus but have a good precalculus background.
- For students who are not quite prepared for MATH 1231, the department offers MATH 1220-1221, a one-year course sequence that combines precalculus with calculus.
- If you took AP Test Calculus AB and received a 4 or 5 (or AB subscore on the BC test), then you have earned credit for MATH 1231. You can take MATH 1232: Calculus II.
- If you took AP Test Calculus BC and received a 4 or 5, then you have earned credit for both MATH 1231 and 1232. You can take MATH 2233: Multivariable Calculus

**Course to take (choose one):**

- MATH 1000: Dean’s Seminar;
- MATH 1007: Mathematics and Politics; or
- MATH 1009: Mathematical Ideas.

These courses are designed for non-technical students who need to meet the G-PAC quantitative reasoning requirement. They provide introductions to topics that are accessible with minimal mathematical background. Students also have the option of taking a statistics course instead of math to meet the requirement.

Note: Calculus keeps academic and career options open that the three courses listed in this section do not, so unless your path is firmly set on a non-technical area, you still may be best served by a calculus course.

**Course to take: **You must take two math courses in a pair (e.g., MATH 1231 and 1232) for the general Bachelor of Science in Business requirements.

**Course to take:** You are required to take one math course, which should be chosen based on your academic goals.

**If you like math or want a minor or second major in a science**, then you should choose a calculus course, MATH 1220, 1231, 1232, 1252 or 2233. For MATH 1220, 1231 and 1252, you need to take the placement test to determine which course best fits your level of preparation. Note that MATH 1252 does not prepare students to continue with MATH 1232, so if you may want to go further with calculus, take MATH 1220 or 1231. If you have AP credit for the prerequisite, you can take MATH 1232 or 2233.

If you only want to satisfy the quantitative reasoning requirement, then you should choose from among Dean’s Seminar (MATH 1000), Mathematics and Politics (MATH 1007) and Mathematical Ideas (MATH 1009). These courses provide introductions to topics that are accessible with minimal mathematical background.

Note: Calculus keeps academic and career options open; MATH 1000, 1007 and 1009 do not. So unless your path is firmly set on a non-technical area, you still may be best served by a calculus course.

**Phillips Hall**

801 22nd St. NW, Room 739

Washington, DC 20052

Phone: 202-994-6235

Email: [email protected]