Noah Aydin joined Kenyon College in 2002 and teaches a range of mathematics and computer science courses. His primary research area is algebraic coding theory. More generally, his research interests include applications of algebra, cryptography, theoretical computer science, mathematics education and history of science. Aydin has been leading a long-term research program in coding theory with Kenyon students that yielded many publications. Aydin and several Kenyon students are record holders for dozens of best-known linear codes. A senior member of IEEE, Aydin has a number of international collaborators and regularly reviews manuscripts for the leading journals in coding theory.

Aydin’s recent interest in the history of mathematics led a multi-volume publication, which is a translation with commentary on one of the most important mathematics books of the medieval Islamic civilization.

Areas of Expertise

Coding theory, cryptography, history of mathematics

Education

2002 — Doctor of Philosophy from The Ohio State University

1997 — Master of Science from The Ohio State University

1996 — Master of Arts from The Ohio State University

1994 — Bachelor of Science from Middle East Tech Univ, TK

Courses Recently Taught

The first in a three-semester calculus sequence, this course covers the basic ideas of differential calculus. Differential calculus is concerned primarily with the fundamental problem of determining instantaneous rates of change. In this course we will study instantaneous rates of change from both a qualitative geometric and a quantitative analytic perspective. We will cover in detail the underlying theory, techniques and applications of the derivative. The problem of anti-differentiation, identifying quantities given their rates of change, also will be introduced. The course will conclude by relating the process of anti-differentiation to the problem of finding the area beneath curves, thus providing an intuitive link between differential calculus and integral calculus. Those who have had a year of high school calculus but do not have advanced placement credit for MATH 111 should take the calculus placement exam to determine whether they are ready for MATH 112. Students who have 0.5 units of credit for calculus may not receive credit for MATH 111. This counts toward the core course requirement for the major. Prerequisite: solid grounding in algebra, trigonometry and elementary functions. Offered every semester.

This course examines an important and interesting part of the history of mathematics and, more generally, the intellectual history of humankind: the history of mathematics in the Islamic world. Some of the most fundamental notions in modern mathematics have their roots here, such as the modern number system, the fields of algebra and trigonometry, and the concept of algorithm, among others. In addition to studying specific contributions of medieval Muslim mathematicians in the areas of arithmetic, algebra, geometry and trigonometry in some detail, we will examine the context in which Islamic science and mathematics arose, and the role of religion in this development. The rise of Islamic science and its interactions with other cultures (e.g., Greek, Indian and Renaissance Europe) tell us much about larger issues in the humanities. Thus, this course has both a substantial mathematical component (60-65 percent) and a significant history and social science component (35-40 percent), bringing together three disciplines: mathematics, history and religion. The course counts toward the Islamic Civilization and Cultures Concentration but does not count toward any math major requirement. Prerequisite: solid knowledge of algebra and geometry.

This course introduces students to mathematical reasoning and rigor in the context of set-theoretic questions. The course will cover basic logic and set theory, relations — including orderings, functions and equivalence relations — and the fundamental aspects of cardinality. The course will emphasize helping students read, write and understand mathematical reasoning. Students will be actively engaged in creative work in mathematics. Students interested in majoring in mathematics should take this course no later than the spring semester of their sophomore year. Advanced first-year students interested in mathematics are encouraged to consider taking this course in their first year. This counts toward the core course requirement for the major. Prerequisite: MATH 213 or permission of instructor. Offered every spring semester.

Combinatorics is, broadly speaking, the study of finite sets and finite mathematical structures. A great many mathematical topics are included in this description, including graph theory, combinatorial designs, partially ordered sets, networks, lattices and Boolean algebras and combinatorial methods of counting, including combinations and permutations, partitions, generating functions, recurring relations, the principle of inclusion and exclusion, and the Stirling and Catalan numbers. This course will cover a selection of these topics. Combinatorial mathematics has applications in a wide variety of nonmathematical areas, including computer science (both in algorithms and in hardware design), chemistry, sociology, government and urban planning; this course may be especially appropriate for students interested in the mathematics related to one of these fields. This counts toward the Discrete/Combinatorial (Column C) elective requirement for the major. Prerequisite: MATH 112 or a score or 4 or 5 on the BC Calculus AP exam or permission of instructor. Offered every other year.

Coding theory, or the theory of error-correcting codes, and cryptography are two recent applications of algebra and discrete mathematics to information and communications systems. The goals of this course are to introduce students to these subjects and to understand some of the basic mathematical tools used. While coding theory is concerned with the reliability of communication, the main problem of cryptography is the security and privacy of communication. Applications of coding theory range from enabling the clear transmission of pictures from distant planets to quality of sound in compact discs. Cryptography is a key technology in electronic security systems. Topics likely to be covered include basics of block coding, encoding and decoding, linear codes, perfect codes, cyclic codes, BCH and Reed-Solomon codes, and classical and public-key cryptography. Other topics may be included depending on the availability of time and the background and interests of the students. Other than some basic linear algebra, the necessary mathematical background (mostly abstract algebra) will be covered within the course. This counts toward either a Discrete/Combinatorial (Column C) or an Algebraic (Column A) elective requirement for the major. Prerequisite: MATH 224 or permission of instructor. Offered every other year.

Abstract algebra is the study of algebraic structures that describe common properties and patterns exhibited by seemingly disparate mathematical objects. The phrase "abstract algebra" refers to the fact that some of these structures are generalizations of the material from high school algebra relating to algebraic equations and their methods of solution. In Abstract Algebra I, we focus entirely on group theory. A group is an algebraic structure that allows one to describe symmetry in a rigorous way. The theory has many applications in physics and chemistry. Since mathematical objects exhibit pattern and symmetry as well, group theory is an essential tool for the mathematician. Furthermore, group theory is the starting point in defining many other more elaborate algebraic structures including rings, fields and vector spaces. In this course, we will cover the basics of groups, including the classification of finitely generated abelian groups, factor groups, the three isomorphism theorems and group actions. The course culminates in a study of Sylow theory. Throughout the semester there will be an emphasis on examples, many of them coming from calculus, linear algebra, discrete math and elementary number theory. There also will be a couple of projects illustrating how a formal algebraic structure can empower one to tackle seemingly difficult questions about concrete objects (e.g., the Rubik's cube or the card game SET). Finally, there will be a heavy emphasis on the reading and writing of mathematical proofs. Junior standing is recommended. This counts toward the Algebraic (Column A) elective requirement for the major. Prerequisite: MATH 222 or permission of instructor. Offered every other fall.

This course picks up where MATH 335 ends, focusing primarily on rings and fields. Serving as a good generalization of the structure and properties exhibited by the integers, a ring is an algebraic structure consisting of a set together with two operations — addition and multiplication. If a ring has the additional property that division is well-defined, one gets a field. Fields provide a useful generalization of many familiar number systems: the rational numbers, the real numbers and the complex numbers. Topics to be covered include polynomial rings; ideals; homomorphisms and ring quotients; Euclidean domains, principal ideal domains, unique factorization domains; the Gaussian integers; factorization techniques and irreducibility criteria. The final block of the semester will serve as an introduction to field theory, covering algebraic field extensions, symbolic adjunction of roots; construction with ruler and compass; and finite fields. Throughout the semester there will be an emphasis on examples, many of them coming from calculus, linear algebra, discrete math and elementary number theory. There also will be a heavy emphasis on the reading and writing of mathematical proofs. This counts toward the Algebraic (Column A) elective requirement for the major. Prerequisite: MATH 335. Offered every other spring.

This course presents an introduction to computer programming intended both for those who plan to take further courses in which a strong background in computation is desirable and for those who are interested in learning basic programming principles. The course will expose the student to a variety of applications where an algorithmic approach is natural and will include both numerical and non-numerical computation. The principles of program structure and style will be emphasized. SCMP 118 may be paired with SCMP 218 or either may be paired with any mathematics or statistics course to satisfy the natural science diversification requirement. No prerequisite. Offered every semester.

This course is intended as a second course in programming, as well as an introduction to the concept of computational complexity and the major abstract data structures (such as dynamic arrays, stacks, queues, link lists, graphs and trees), their implementation and application, and the role they play in the design of efficient algorithms. Students will be required to write a number of programs using a high-level language. SCMP 218 may be paired with SCMP 118 or either may be paired with any mathematics or statistics course to satisfy the natural science diversification requirement. Prerequisite: SCMP 118, MATH 138 or PHYS 270 or permission of instructor. Offered every other spring.