# Courses

#### Course Numbering

0-99 Advanced Placement Credit; House Courses; First-Year Seminars; First-Year Writing; Registrar/Department special purpose

100-199 Introductory-level undergraduate courses; basic skills/activity courses; foundation courses; Focus program courses

200-399 Undergraduate courses above introductory level

400-499 Advanced undergraduate, senior seminars, capstone courses, honors thesis courses

500-699 Graduate courses open to advanced undergraduates

700-999 Graduate only courses (not open to undergraduates)

- All Courses
- Featured Courses
- Calculus & Engineering Math Courses
- Courses by Math Field
- Courses by Career Track

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH89S | Game Theory and Democracy | QS, R, STS | |

MATH190S | Game Theory and Democracy | STS | |

MATH218 | Matrices and Vector Spaces | QS | |

MATH240 | Introduction to Applied Mathematics: Modeling, Equations and Proofs | QS | |

MATH245 | Introduction to Mathematics: Example, Conjecture, and Proof | QS | |

MATH305S | Number Theory | QS, R | ISIS305S |

MATH403 | Advanced Linear Algebra | QS | |

MATH477S | Seminar in Mathematical Modeling with a Focus on Writing | QS, R, W | |

MATH490 | Introduction to Category Theory and Mathematized Thinking | QS, R |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH21 | Introductory Calculus I | ||

MATH22 | Introductory Calculus II | ||

MATH105L | Laboratory Calculus and Functions I | QS | |

MATH106L | Laboratory Calculus and Functions II | QS | |

MATH111L | Laboratory Calculus I | QS | |

MATH112L | Laboratory Calculus II | QS | |

MATH121 | Introductory Calculus I | QS | |

MATH122 | Introductory Calculus II | QS | |

MATH122L | Introductory Calculus II with Applications | QS | |

MATH202 | Multivariable Calculus for Economics | QS | |

MATH212 | Multivariable Calculus | QS | |

MATH216 | Linear Algebra and Differential Equations | QS | |

MATH222 | Advanced Multivariable Calculus | QS | |

MATH353 | Ordinary and Partial Differential Equations | QS |

- Algebra & Combinatorics
- Analysis
- Biological Modeling
- Computational Mathematics
- Geometry: Differential & Algebraic
- Mathematical Physics
- Number Theory
- PDE & Dynamical Systems
- Physical Modeling
- Probability
- Signals, Images & Data
- Topology
- Calculus & Engineering Math Courses

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH21 | Introductory Calculus I | ||

MATH22 | Introductory Calculus II | ||

MATH111L | Laboratory Calculus I | QS | |

MATH112L | Laboratory Calculus II | QS | |

MATH121 | Introductory Calculus I | QS | |

MATH122 | Introductory Calculus II | QS | |

MATH122L | Introductory Calculus II with Applications | QS | |

MATH202 | Multivariable Calculus for Economics | QS | |

MATH212 | Multivariable Calculus | QS | |

MATH222 | Advanced Multivariable Calculus | QS | |

MATH375 | Introduction to Linear Programming and Game Theory | QS | |

MATH421 | Differential Geometry | QS | |

MATH431 | Advanced Calculus I | QS, W | |

MATH531 | Real Analysis I | QS, W | |

MATH532 | Basis Analysis II | QS | |

MATH551 | Applied Partial Differential Equations and Complex Variables | QS | |

MATH553 | Asymptotic and Perturbation Methods | QS | |

MATH625 | Riemann Surfaces | QS | |

MATH631 | Measure and Integration | QS | |

MATH633 | Complex Analysis | QS | |

MATH635 | Functional Analysis | QS | |

MATH690-30 | Topics in Complex Analysis | QS | |

MATH690-32 | Topics in Analysis | ||

MATH790-30 | Current Research in Analysis |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH168S | Mathematical Investigations in Genetics and Genomics | QS | GENOME168S |

MATH240 | Introduction to Applied Mathematics: Modeling, Equations and Proofs | QS | |

MATH476S | Seminar in Mathematical Modeling | QS, R | |

MATH477S | Seminar in Mathematical Modeling with a Focus on Writing | QS, R, W | |

MATH573S | Modeling of Biological Systems | QS, R | CBB573S |

MATH790-71 | Current Research in Applied Mathematics | ||

MATH790-77 | Current Research in Mathematical Biology |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH361 | Mathematical Numerical Analysis | QS | |

MATH361S | Mathematical Numerical Analysis | QS, R | |

MATH561 | Numerical Linear Algebra, Optimization and Monte Carlo Simulation | QS | |

MATH563 | Applied Computational Analysis | QS | |

MATH565 | Numerical Analysis | QS, R | COMPSCI520, STAT612 |

MATH660 | Introduction to Numerical PDEs | QS | |

MATH661 | Numerical Solution of Hyperbolic Partial Differential Equations | QS | |

MATH663 | Numerical Solution of Elliptic and Parabolic Partial Differential Equations | QS |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH323S | Geometry | R | |

MATH421 | Differential Geometry | QS | |

MATH527 | General Relativity | NS, QS | PHYSICS622 |

MATH625 | Riemann Surfaces | QS | |

MATH627 | Algebraic Geometry | QS | |

MATH690-00 | Topics in Algebraic Geometry | ||

MATH690-20 | Topics in Differential Geometry | QS | |

MATH790-03 | Research in Algebraic Geometry | ||

MATH790-20 | Current Research in Differential Geometry |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH527 | General Relativity | NS, QS | PHYSICS622 |

MATH790-73 | Current Research in Mathematical Physics |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH165S | Cryptography and Society | QS, STS, W | GENOME165FS. |

MATH305 | Number Theory | QS | |

MATH305S | Number Theory | QS, R | ISIS305S |

MATH404 | Mathematical Cryptography | QS | |

MATH605 | Algebraic Number Theory | ||

MATH690-05 | Topics in Number Theory |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH240 | Introduction to Applied Mathematics: Modeling, Equations and Proofs | QS | |

MATH476S | Seminar in Mathematical Modeling | QS, R | |

MATH477S | Seminar in Mathematical Modeling with a Focus on Writing | QS, R, W | |

MATH551 | Applied Partial Differential Equations and Complex Variables | QS | |

MATH553 | Asymptotic and Perturbation Methods | QS | |

MATH575 | Mathematical Fluid Dynamics | QS | |

MATH790-71 | Current Research in Applied Mathematics |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH182FS | Mathematics of Finance | QS | |

MATH230 | Probability | QS | STAT230 |

MATH333 | Complex Analysis | QS | |

MATH340 | Advanced Introduction to Probability | QS | STAT231 |

MATH541 | Applied Stochastic Processes | QS | STAT621 |

MATH545 | Introduction to Stochastic Calculus | QS | |

MATH581 | Mathematical Finance | QS | ECON673 |

MATH641 | Probability | QS | |

MATH690-40 | Topics in Probability Theory | QS | STAT690-40 |

MATH690-82 | Topics in Mathematical Finance | ECON690-82 | |

MATH742 | Stochastic Models | ||

MATH743 | Linear Models | STAT721 |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH218 | Matrices and Vector Spaces | QS | |

MATH218L (primary) | Matrices & Vector Spaces (LAB) | QS | |

MATH230 | Probability | QS | STAT230 |

MATH238L | Data Analysis and Decision Science | QS | |

MATH340 | Advanced Introduction to Probability | QS | STAT231 |

MATH375 | Introduction to Linear Programming and Game Theory | QS | |

MATH403 | Advanced Linear Algebra | QS | |

MATH465 | Introduction to High Dimensional Data Analysis | QS | COMPSCI445 |

MATH541 | Applied Stochastic Processes | QS | STAT621 |

MATH561 | Numerical Linear Algebra, Optimization and Monte Carlo Simulation | QS |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH411 | Topology | QS | |

MATH412 | Topological Data Analysis | QS | COMPSCI434 |

MATH611 | Algebraic Topology I | QS | |

MATH612 | Algebraic Topology II | QS | |

MATH690-10 | Topics in Topology | ||

MATH790-10 | Current Research in Topology |

Course Number | Title | Curriculum Codes | Crosslisting Numbers |
---|---|---|---|

MATH21 | Introductory Calculus I | ||

MATH22 | Introductory Calculus II | ||

MATH105L | Laboratory Calculus and Functions I | QS | |

MATH106L | Laboratory Calculus and Functions II | QS | |

MATH111L | Laboratory Calculus I | QS | |

MATH112L | Laboratory Calculus II | QS | |

MATH121 | Introductory Calculus I | QS | |

MATH122 | Introductory Calculus II | QS | |

MATH122L | Introductory Calculus II with Applications | QS | |

MATH202 | Multivariable Calculus for Economics | QS | |

MATH212 | Multivariable Calculus | QS | |

MATH216 | Linear Algebra and Differential Equations | QS | |

MATH222 | Advanced Multivariable Calculus | QS | |

MATH353 | Ordinary and Partial Differential Equations | QS |

- For Actuarial Science
- For Business & Economics
- For Computer Science
- For Engineering & Natural Sciences
- For Graduate Math Study
- For Statistics & Operations Research
- For Teaching Math

## For Actuarial Science

An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries mathematically evaluate the probability of events and quantify the contingent outcomes in order to minimize the impacts of financial losses associated with uncertain undesirable events. The profession has consistently ranked as one of the most desirable in various studies over the years.

Actuaries can earn professional status by passing a series of examinations administered by the Society of Actuaries (SOA) and Casualty Actuarial Society (CAS). The first two exams are:

- ExamP: Probability
- ExamFM: Financial Mathematics

Previous versions of these exams, with answer keys and solutions, and information about submitting an application for the exams, can be found online at Be An Actuary.

The CAS Syllabus of Examinations and the Education Area of the SOA web site contain a description of the education and examination system for the Preliminary Actuarial Examinations, including the material to be covered for each examination, instructions, schedules, and applications. Students can find links to this information at Be An Actuary.

The optimal time to take the first exam is soon after completing a calculus-based probability course such as MATH 230 Probability or MATH 340 Advanced Introduction to Probability. The following is a list of Duke courses that are useful in preparing for a career as an actuary.

- MATH 230 Probability or MATH 340 Advanced Introduction to Probability
- MATH 342D Statistics
- MATH 541 Applied Stochastic Processes
- MATH 581 Mathematical Finance
- MATH 582 Financial Derivatives
- ECON 210D Intermediate Economics III
- ECON 208D Introduction to Econometrics
- ECON 471 Financial Markets and Management
- STA 210 Regression Analysis
- STA 831 Probability and Statistical Methods
- STA 721 Linear Models

As part of Preliminary Education in both the SOA and the CAS, there are three subject areas that require Validation by Educational Experience (VEE): Economics (macro and micro), Mathematical Statistics, and Accounting & Finance. A directory of approved college courses is available at the VEE requirements home page. You may apply for VEE credit for your coursework after you have passed the first two exams.

If you are pursuing the SOA career path, you will start the Fundamentals of Actuarial Practice (FAP) course after you finish the Preliminary Education requirements. FAP is an e-Learning course that includes both online and offline activities and exposes you to real-world situations.

For further information or additional advice about careers in the actuarial sciences, please contact Professor Amy Herring of the Department of Statistical Science, Duke math alumnus Emily Reither, now at Allstate, or alumnus Andrew Tignanelli.

The curriculum in Statistics and Operations Research at UNC-Chapel Hill includes an Actuarial Science option through which students take specialized courses – STOR 471 Long Term Actuarial Models (fall semester) and STOR 472 Short Term Actuarial Models (spring semester). Descriptions of these courses can be found on the UNC curriculum website. Under a reciprocal agreement between the two universities, students at Duke may enroll concurrently in these courses offered by UNC. Note, however, that prior approval from the Director of Undergraduate Studies must be sought for such courses to count toward mathematics major or minor credit. Charles W. Dunn, a Duke graduate and Fellow of the Society of Actuaries, teaches the UNC courses and will be happy to answer questions about them or about actuarial science in general.

Duke students are also welcome to participate in activities sponsored by Carolina's Actuarial Student Organization (UNC CASO), an undergraduate student actuarial club. Check out their website for more information.

## For Business and Economics

Many professions and many graduate and professional school programs regard a strong background in mathematics as highly desirable. For that reason, students with a primary interest in other disciplines may also want to consider a major or minor in mathematics.

For students interested in Business or Economics, the following courses are recommended:

## For Computer Science

Many professions and many graduate and professional school programs regard a strong background in mathematics as highly desirable. For that reason, students with a primary interest in other disciplines may also want to consider a major or minor in mathematics.

For students interested in Computer Science, the following courses are recommended:

- MATH 218 Matrices and Vector Spaces
- MATH 361S Mathematical Numerical Analysis
- MATH 371 Combinatorics
- MATH 375 Introduction to Linear Programming and Game Theory
- MATH 403 Advanced Linear Algebra
- MATH 465 Introduction to High Dimensional Data Analysis
- MATH 487 Introduction to Mathematical Logic
- MATH 388 Logic and Its Applications
- MATH 501 Introduction to Algebraic Structures I
- and possibly MATH 502 Introduction to Algebraic Structures 2

## For Engineering & Natural Sciences

Many professions and many graduate and professional school programs regard a strong background in mathematics as highly desirable. For that reason, students with a primary interest in other disciplines may also want to consider a major or minor in mathematics.

For students interested in Engineering or Natural Sciences, the following courses are recommended:

- MATH 356 Elementary Differential Equations
- MATH 451S Nonlinear Ordinary Differential Equations
- MATH 453 Introduction to Partial Differential Equations
- MATH 431 Advanced Calculus I
- MATH 333 Complex Analysis
- MATH 476S Seminar in Mathematical Modeling
- MATH 531 Basic Analysis I
- MATH 532 Basic Analysis II
- MATH 551 Applied Partial Differential Equations and Complex Variables
- MATH 541 Applied Stochastic Processes
- MATH 561 Numerical Linear Algebra, Optimization and Monte Carlo Simulation

## For Graduate Math Study

A student planning to pursue graduate study in mathematics should develop a program of study that provides both variety of experience and a strong background in fundamental areas. The core courses for either pure or applied mathematics are:

- MATH 333 Complex Analysis
- MATH 501 Introduction to Algebraic Structures I (taken no later than the junior year)
- MATH 502 Introduction to Algebraic Structures II (taken no later than the junior year)
- MATH 531 Basic Analysis I or MATH 532 Basic Analysis II (taken no later than the junior year)

Recommended courses are:

Students interested in applied mathematics should consider:

- MATH 451S Nonlinear Ordinary Differential Equations
- MATH 453 Introduction to Partial Differential Equations
- MATH 230 Probability
- MATH 342D Statistics
- MATH 361S Mathematical Numerical Analysis
- MATH 476S Seminar in Mathematical Modeling
- MATH 581 Mathematical Finance
- MATH 541 Applied Stochastic Processes
- MATH 561 Numerical Linear Algebra, Optimization and Monte Carlo Simulation

Advanced students are encouraged to take standard graduate level courses (numbered 555 and above) in their senior (and occasionally in their junior) years. In particular, the following are recommended:

Graduate programs usually expect that applicants will take the Graduate Record Examination Subject Test in mathematics. The test emphasizes linear algebra, abstract algebra, and advanced calculus, but also includes questions about complex analysis, topology, combinatorics, probability, statistics, number theory, and algorithmic processes.

## For Statistics and Operations Research

At present, job prospects are good at all degree levels for those with a strong background in statistics and some computer programming experience. A student interested in pursuing statistics or operations research has several academic options. Duke offers a major in statistical science through the Department of Statistical Science or, alternatively, students can major in math with an emphasis in statistics.

For further information, contact the Director of Undergraduate Studies in Statistical Science at dus@stat.duke.edu.

##### Going Straight to the Workforce

For students who DO NOT intend to pursue graduate work, the following courses are recommended:

- MATH 218 Matrices and Vector Spaces
- MATH 230 Probability
- MATH 342D Statistics
- MATH 581 Mathematical Finance
- COMPSCI 101 Program Design and Analysis I
- COMPSCI 201 Data Structures and Algorithms

With at least some of the following electives:

- MATH 541 Applied Stochastic Processes
- MATH 361S Mathematical Numerical Analysis
- MATH 565 Numerical Analysis
- COMPSCI 308 Software Design and Implementation

##### Pursuing Graduate Work

For students who DO plan to pursue graduate work in statistics or operations research, having a strong background in mathematics (especially analysis and linear algebra) and computer science is the best course of action. The following is recommended:

- Major in math and take the core course sequence recommended for students planning to pursue graduate mathematics study

Taking at least some of the following electives:

## For Teaching Math

For students planning to pursue careers as secondary school math teachers, the following courses are recommended:

- MATH 323S Geometry
- MATH 431 Advanced Calculus I or MATH 531 Basic Analysis I
- MATH 401 Introduction to Abstract Algebra or MATH 501 Introduction to Algebraic Structures I
- COMPSCI 94 Programming and Problem Solving or COMPSCI 101 Program Design and Analysis I
- MATH 230 Probability or MATH 340 Advanced Introduction to Probability/Math 342D Statistics

The following courses would also be helpful:

- MATH 371 Combinatorics
- MATH 487 Introduction to Mathematical Logic
- MATH 305S Number Theory
- MATH 476S Seminar in Mathematical Modeling
- MATH 356 Elementary Differential Equations
- Two courses in physics such as PHYSICS 25 Physics I and 26 Physics II (AP Credit), or PHYSICS 1441L General Physics I and 142L General Physics II, or PHYSICS 151L Introductory Mechanics and 152L Introductory Electricity, Magnetism and Optics, or PHYSICS 161D Fundamentals of Physics I and 162D Fundamentals of Physics II.

#### Teaching Credentials and Eligibility

There are a couple of ways in which a student can major in mathematics and also to be qualified to teach.

##### Math Teaching License

A student with an interest in teaching at the high school level is encouraged to earn a Math Teaching License while working on their requirements for their mathematics major.

The teaching license, which is earned by fulfilling requirements prescribed by the State of North Carolina, is generally accepted in most of the 50 states by reciprocal agreement. Schools are now required by federal mandate to ensure that teachers hold appropriate licensure in their respective content area with the goal of having all classrooms led by highly qualified professionals.

Requirements for the Math Teaching License include a variety of education courses, a psychology course, and other courses in mathematics. Students who complete the licensure program also earn a minor in Education.

The last semester of the senior year is devoted to the student teaching block. This includes two education courses and 10-12 weeks of full-time teaching and observation in a Durham Public School, working with a licensed high school teacher and PiE faculty. The student teaching practicum counts as two course credits.

Because of the time constraints this may impose on the planning of courses, students who consider teaching high school math should confer with the faculty in the Program in Education prior to preparing a long-range plan.

##### Master of Arts in Teaching (MAT) Program

A student may complete their undergraduate degree in mathematics and apply to the Graduate School to obtain a master of arts in teaching (MAT). A MAT degree prepares one for a secondary school teaching position, with an advanced pay scale. Many junior colleges employ teachers who hold these degrees.

Duke has one of the most innovative MAT Programs in the country. It is virtually unique with an emphasis on extensive classroom experience and advanced mathematics courses rather than on education courses.

The MAT Program has recently received a 3-year grant from the National Science Foundation that awards fellowships to students who complete the MAT program in mathematics. The only requirement upon completion of the program is to serve two years teaching mathematics in a high-need school. Please note that Durham Public Schools qualify as high-need.

For more information about this program contact the director, Alan Teasley or any of the teaching faculty in the Mathematics Department.

##### Teaching Math in a Private School

To teach in a private school, only an undergraduate degree with a major or minor in mathematics may be required; however, a mathematics major is highly recommended.