Nuh (Noah) Aydin joined the Kenyon faculty in 2002. His primary research area is algebraic coding theory. More generally, his research interests include applications of algebra, finite fields, cryptography, combinatorics, theoretical computer science and history and philosophy of science. Additionally, he is interested in pedagogy and mathematics education.

Noah teaches a wide range of mathematics courses as well as introductory computer science courses at Kenyon. He enjoys working with undergraduates on mathematical research and has published several papers with Kenyon undergraduates. He has two daughters and a son, enjoys playing soccer and has a great interest in meteorology.

### Areas of Expertise

Algebraic Coding Theory, finite fields, cryptography, history of mathematics in the Islamic World.

### 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

MATH 111

## Calculus I

#### MATH 111

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 .5 unit of credit for calculus may not receive credit for MATH 111. Prerequisite: solid grounding in algebra, trigonometry and elementary functions. Offered every semester.

MATH 112

## Calculus II

#### MATH 112

The second in a three-semester calculus sequence, this course has two primary foci. The first is integration, including techniques of integration, numerical methods and applications of integration. This study leads into the analysis of differential equations by separation of variables, Euler's method and slope fields. The second focus is the notion of convergence, as manifested in improper integrals, sequences and series, particularly Taylor series. Prerequisite: MATH 111 or AP score of 4 or 5 on Calculus AB exam or an AB subscore of 4 or 5 on the Calculus BC exam or permission of instructor. Offered every semester.

MATH 118

## Introduction to Programming

#### MATH 118

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. Offered every semester.

MATH 128

## History of Mathematics in the Islamic World

#### MATH 128

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 is a part of the Islamic Civilization and Cultures Program and fulfills the QR requirement. No prerequisite is needed beyond high school algebra and geometry but solid knowledge in algebra and geometry is needed.

MATH 191

## ST:Hist of Math/Islamic World

#### MATH 191

MATH 218

## Data Structures and Program Design

#### MATH 218

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. Prerequisite: SCMP 118 or permission of instructor. Offered every other spring.

MATH 227

## Combinatorics

#### MATH 227

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. Prerequisite: MATH 112 or a score or 4 or 5 on the BC Calculus AP exam or permission of instructor. Offered every other year.

MATH 328

## Coding Theory and Cryptography

#### MATH 328

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. Prerequisite: MATH 224 or permission of instructor. Offered every other year.

MATH 335

## Abstract Algebra I

#### MATH 335

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. Prerequisite: MATH 222 or permission of instructor. Offered every other fall.

MATH 435

## Abstract Algebra II

#### MATH 435

Abstract Algebra II 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. Prerequisite: MATH 335. Offered every other spring.

MATH 493

## Individual Study

#### MATH 493

Individual study is a privilege reserved for students who want to pursue a course of reading or complete a research project on a topic not regularly offered in the curriculum. It is intended to supplement, not take the place of, coursework. Individual study cannot be used to fulfill requirements for the major. Individual studies will earn 0.25 – 0.50 units of credit. To qualify, a student must identify a member of the mathematics department willing to direct the project. The professor, in consultation with the student, will create a tentative syllabus (including a list of readings and/or problems, goals and tasks) and describe in some detail the methods of assessment (e.g., problem sets to be submitted for evaluation biweekly; a 20-page research paper submitted at the course's end, with rough drafts due at given intervals, and so on). The department expects the student to meet regularly with his or her instructor for at least one hour per week. All standard enrollment/registration deadlines for regular college courses apply. Because students must enroll for individual studies by the end of the seventh class day of each semester, they should begin discussion of the proposed individual study preferably the semester before, so that there is time to devise the proposal and seek departmental approval before the registrar's deadline. Permission of instructor and department chair required. No prerequisite.\n\n

SCMP 118

## Introduction to Programming

#### SCMP 118

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 a mathematics or statistics course for diversification purposes. Offered every semester.

SCMP 218

## Data Structures and Program Design

#### SCMP 218

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. Prerequisite: SCMP 118 or PHYS 270 or permission of instructor. Offered every other spring.

SCMP 401

## Scientific Computing Seminar

#### SCMP 401

This capstone course is intended to provide an in-depth experience in computational approaches to science. Students will work on individual computational projects in various scientific disciplines. Each student will give several presentation to the class throughout the semester. Prerequisite: SCMP 118 or PHYS 270, completion of at least .5 unit of an "intermediate" course and at least .5 unit of a contributory course, senior standing, and permission of the instructor and the program director.

SCMP 493

## Individual Study

#### SCMP 493

The Individual Study is to enable students to explore a pedagogically valuable topic in computing applied to the sciences that is not part of a regularly offered SCMP course. A student who wishes to propose an individual study course must first find a SCMP faculty member willing to supervise the course. The student and faculty member then craft a course syllabus that describes in detail the expected coursework and how a grade will be assigned. The amount of credit to be assigned to the IS course should be determined with respect to the amount of effort expected in a regular Kenyon class. The syllabus must be approved by the director of the SCMP program. In the case of a small group IS, a single syllabus may be submitted and all students must follow the same syllabus. Permission of the instructor and the program director are required. Because students must enroll for individual studies by the end of the seventh class day of each semester, they should begin discussion of the proposed individual study preferably the semester before, so that there is time to devise the proposal and seek departmental approval before the registrar’s deadline. No prerequisite. \n

### Academic & Scholarly Achievements

2011

"New quinary linear codes from quasi-twisted codes and their duals" Applied Mathematics Letters, Vol 24, No 4, pp 512-515, April 2011 (co-authered with Kenyon undergraduate Ryan Ackerman)

2010

"On the construction of skew quasi-cyclic codes" IEEE Transactions on Information Theory, Vol. 56, No. 5, pp. 2081-2090, May 2010 (with T. Abualrub, A. Ghrayeb and I. Siap)

2009

"Enhancing Undergraduate Curriculum via Coding Theory and Cryptography", PRIMUS (Problems, Resources and Issues in mathematic undergraduate studies) Volume 19 Issue 3, 296-309, May 2009.

2007

"A search algorithm for linear codes", Designs, Codes and Cryptography, 45:2, pp 213-217, November 2007 (co-authered with Kenyon undergraduate Tsvetan Asamov)

2007

"An Introduction to Coding Theory via Hamming Codes", A Computational Science Module developed as part of an NSF grant. August 2007.

2004

"On some classes of optimal and near-optimal polynomial codes", Finite Fields and Their Applications. Vol. 10 , No. 1 , pp. 24-35, January 2004 (with D. Ray-Chaudhuri)

2003

"Remote Belief: Preserving Volition for Loosely-Coupled Processes", in proceedings of ICDCS 2003, 23 rd International Conference on Distributed Computing Systems, Providence, Rhode Island, pp. 434-440, May 19-22, 2003 (with P. A. Sivilotti)