Mathematics
Overview
The Mathematics Area of Concentration (AOC) at New College is both challenging and exciting. Students are exposed to a broad range of mathematical disciplines from linear and abstract algebra to analysis and differential equations. They develop strong critical thinking and problem-solving skills, the ability to produce rigorous mathematical proofs, and a deep understanding of powerful mathematical theories having many applications as well as their own internal beauty.
A variety of courses and tutorials on advanced topics are available, giving mathematics majors the opportunity to work on advanced material often found in graduate school offerings. Students are able to take courses and tutorials in topology, discrete mathematics, graph theory, probability, geometry, and number theory, as well as in computer science and other sciences. Students concentrating in mathematics often have the opportunity to participate in summer research programs. To attain a broad education, students are encouraged to foray into other liberal arts courses in the humanities and social sciences as well.
An essential element of the Mathematics program is participation in the Mathematics Seminar, a longstanding New College tradition. Offered every semester, this seminar provides a forum for math majors as well as non-majors to listen to talks on mathematically related topics alongside fellow students and the Mathematics faculty.
(See also Applied Mathematics)
Faculty in Mathematics
Christopher Kottke, Associate Professor of Mathematics
Patrick McDonald, Professor of Mathematics
Eirini Poimenidou, Professor of Mathematics (On Leave)
Vlad Serban, Visiting Assistant Professor of Mathematics
Necmettin Yildirim, Professor of Mathematics/Soo Bong Chae Chair of Applied Mathematics
Requirements for the AOC in Mathematics
A minimum of twelve and one-half (12.5) academic units.
| Code | Title |
|---|---|
| Core Requirements | |
| Calculus I | |
or MATH 3472 | Calculus with Theory I |
| Calculus II* | |
or MATH 3473 | Calculus with Theory II |
| Calculus III | |
| Linear Algebra | |
or MATH 4015 | Advanced Linear Algebra |
| Ordinary Differential Equations | |
| Probability I and Probability II 1 | |
| Programming Course | |
| Select one from the following examples: | |
| Introduction to Programming in Python | |
| Object-Oriented Programming | |
| Functional Programming in Haskell* | |
| Additional Math Requirements | |
| Real Analysis I* | |
| Abstract Algebra I | |
| Mathematics Seminar (Three Semesters) 2 | |
| Electives | |
| Select two upper-level courses from the following examples: | |
| Real Analysis II | |
| Abstract Algebra II | |
| Complex Analysis | |
| Introduction to Number Theory with Applications to Cryptography* | |
| Graph Theory* | |
| Point-Set Topology | |
| Advanced Linear Algebra (If not also used for Linear Algebra requirement) | |
| Partial Differential Equations | |
| Basic Set Theory* | |
| Introduction to Numerical Methods | |
| Mathematical Modeling | |
| Advanced Topics: Analysis | |
| Advanced Topics: Algebra | |
| Advanced Topics: Probability | |
| Advanced Topics: Geometry/Topology | |
| Advanced Topics: Applied Math | |
| Additional Requirement | |
| Senior Thesis in Mathematics and Baccalaureate Exam | |
- 1
These are each one-mod courses; together they count as one academic unit.
- 2
To receive mod course credit (.5 unit) for the Mathematics Seminar, students must prepare and present a talk at one of the seminar sessions. One of the most important roles of the Mathematics Seminar, in addition to honing students' communication skills, has been to build a sense of community in the program.
Requirements for a Secondary Field in Mathematics
A minimum of six and one-half (6.5) academic units.
| Code | Title |
|---|---|
| Core Requirements | |
| Calculus I | |
or MATH 3472 | Calculus with Theory I |
| Calculus II* | |
or MATH 3473 | Calculus with Theory II |
| Calculus III | |
or MATH 3330 | Ordinary Differential Equations |
| Linear Algebra | |
| Additional Math Requirements | |
| Real Analysis I* | |
or MATH 4301 | Abstract Algebra I |
| Mathematics Seminar (One Semester) 1 | |
| Elective | |
| Select one upper-level course from the following examples: | |
| Real Analysis II | |
| Abstract Algebra II | |
| Complex Analysis | |
| Introduction to Number Theory with Applications to Cryptography* | |
| Graph Theory* | |
| Point-Set Topology | |
| Optional | |
| A programming course is highly recommended. | |
- 1
To receive mod course credit (.5 unit) for the Mathematics Seminar, students must prepare and present a talk at one of the seminar sessions. One of the most important roles of the Mathematics Seminar, in addition to honing students' communication skills, has been to build a sense of community in the program.
Mathematics Facilities
The Mathematics program at New College has built a strong sense of community, resting in part on the existence of a place for faculty and students to gather and do mathematics–the Math Reading Room (Heiser Natural Sciences 106). This large seminar/study room is used for an active schedule of seminars, presentations, workshops, problem sessions, tutorials, and discussions. This stimulating interaction is highly valued by students and contributes greatly to their growth and development in mathematics.
Representative Senior Theses in Mathematics
- The Heat Content of Triangles
- Normal Power Graphs of Finite Groups
- Torsional Rigidity and Infinite Sums
- Lorentz Violation in the Collective Excitations of Condensates
- Faith and Confidence in New Age Markets: Cryptocurrencies and Stock Bubbles
- Knot Theory and the Alexander Polynomial
- Discretization of Regular Surfaces Preserving Curvature
- Topological K-Theory and Bott Periodicity
- More Rings More Problems: A Discussion of Number Fields for Homomorphic Cryptography
- Solutions to the Oberwolfach Problem and Odd Coverings of Graphs
- Mathematical Linguistics: The Pumping Lemma and Classification of Natural Languages
- The Stability of Theories from Categoricity to their Spectrum
- Abstract Synecdoche in Finite Semigroups: A General Theory of Pointlike Sets and Related Phenomena
- Methods in Tiling with subsets of Zn
- Group Ring Cryptography