ASSOCIATE PROFESSOR

Eric Gottlieb. 1998. E.C. Ellett Chair of Mathematics. B.S., Antioch College; M.S., University of Washington; Ph.D., University of Miami. (Algebraic combinatorics.) ASSISTANT PROFESSORS
Rachel M. Dunwell. 2005. B.Sc., Leeds University; M.Sc., Liverpool University; Ph.D., Heriot-Watt University. (Dynamical Systems, Psychometrics.)
Christopher Mouron. 2002. B.S., Lafayette College; M.S. and Ph.D., Texas Tech University. (Topology, continuum theory, discrete dynamical systems.)
Chris Seaton. 2004. B.A., Kalamazoo College; Ph.D., University of Colorado at Boulder. (Orbifold differential geometry.)
 R. Patrick Vernon.  2007. B.S., Tennessee Technological University: M.S. and Ph.D., Tulane University. (Continum Theory, Topology).
Betsy Williams. 2007. B.S., Millsaps College, M.S. and Ph.D. candidate, Vanderbilt University. (Computer graphics and animation.)

STAFF

K. Michelle Hammontree. Departmental Assistant. B.A., University of Southern Indiana, Evansville.

REQUIREMENTS FOR A MAJOR IN MATHEMATICS LEADING TO THE B.S. DEGREE

A total of fifty-seven (57) credits as follows:

1. Mathematics 121, 122, 201, 223, 261, 321, 362, 386, 485, and 486.
2. Computer Science 141.
3. Physics 111, 111L, 112, and 112L.
4. Three additional four-credit mathematics courses numbered above 200, excluding 495 and 496.
   

REQUIREMENTS FOR A MAJOR IN COMPUTER SCIENCE LEADING TO THE B.S. DEGREE

A total of fifty-six (56) credits as follows:

1. Computer Science 141, 142, 172, 231, 241, 485, and 486.
2. Mathematics 121, 122, and either 223 or 261.
3. One computer science course from each of the following groups: Systems (330 to 340), and Theory (350 to 360).
4. Three additional four-credit computer science courses numbered above 300, excluding 495 and 496.
   

REQUIREMENTS FOR A MINOR IN MATHEMATICS

A total of twenty-four (24) credits as follows:

1. Mathematics 121, 122, 201, 223, and 261.
2. One additional four-credit mathematics course numbered above 300.
   

REQUIREMENTS FOR A MINOR IN COMPUTER SCIENCE

A total of twenty-four (24) credits as follows:

1. Computer Science 141, 142, 172, 231, and 241.
2. One additional four-credit computer science course numbered above 300.
   

HONORS IN MATHEMATICS OR COMPUTER SCIENCE:

1. Required courses: fulfillment of the requirements for the major.
2. Honors course: readings, research, and a research and/or expository thesis.
3. Approval by the department is required.
   

PLANNING A MAJOR

Students considering a major in Mathematics or Computer Science should contact the Chair or another member of the department as early as possible to ensure progress is being made toward the major. More information can be found at the department’s web site: www.rhodes.edu/mathcs.

For reasonable progress toward a major in Mathematics, a student should begin the Calculus sequence (Math 121, 122 and 223) at the appropriate level in the first year, and complete the sequence before the Spring of the second year; complete Math 201 in the first year (or second year if necessary); and by the end of the second year, complete Math 261, Computer Science 141, and the Physics sequence.

For reasonable progress toward a major in Computer Science, a student should begin the introductory programming sequence (Computer Science 141, 142, 241) in the first year. In the second year, a student should complete Computer Science 172 in fall and Computer Science 231 in the spring. The Mathematics requirements should be completed by the end of the third year.

COURSE OFFERINGS

105. Topics in Mathematics.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science.
A course designed for the non-mathematics major. Possible topics may include (but are not restricted to) music and math and mathematical modeling.
Prerequisites: Minimal, depending on the topic.

107. Linear Methods.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
Topics include systems of linear equations, matrices, matrix inversion and applications (including Leontief input-output analysis), mathematical programming, linear programming and the simplex method, finite Markov chains, and game theory.
Prerequisites: None.

108. Cryptology.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
This course is an examination of conventional cryptographic methods (such as substitution and transposition ciphers), public key methods (such as RSA, a standard method for secure web transactions), and computer-based conventional cryptographic techniques (block ciphers and hash functions). We will develop and use mathematical tools such as modular arithmetic, probability, matrix algebra, and number theory both to implement and cryptanalyze these methods. In addition, we will deal with a few of the technical and public policy issues surrounding uses of encryption.
Prerequisites: None.

111. Elementary Probability and Statistics.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
This course includes the following topics: descriptive statistics, sample spaces, counting procedures, compound events, random variables, discrete and continuous probability distributions, expectation, estimation, hypothesis testing, correlation, and simple linear regression. Computer statistical packages will be used. Students who have already had Math 122 should consider taking Math 311-312 instead.
Prerequisites: None.

115. Applied Calculus.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
This one-semester course presents an introduction to applied mathematics and an overview of calculus: applications of the derivative, the definite Integral, the Fundamental Theorem of Calculus, partial derivatives and double integrals. Applications will involve the use of a variety of functions, including exponential, logarithmic and trigonometric functions. Each topic is introduced through the modeling process; computer-based applications and group work are major components of this course. (Note: Students who have already had Math 121 may not earn credit for Math 115. Math 115 is not adequate preparation for Math 122.)
Prerequisites: None.

121. Calculus I.
Fall. Credits: 4.
Degree Requirements: Natural Science, F6.
This course is an introduction to the concepts, formalism, and applications of derivatives and integrals. Elementary transcendental functions are used throughout; specific topics include limits, the derivative, applications of differentiation, the definite integral, and the Fundamental Theorem of Calculus.
Prerequisites: Students will need a background in high school algebra, geometry, trigonometry, and exponential and logarithmic functions.

122. Calculus II.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
This course is an introduction to (1) formal and numerical techniques of integration, (2) Taylor’s theorem, sequences, series, power series, and their applications, (3) applications of integration and series to solving first-order and linear differential equations, and (4) applications of integration to calculate area, length, volume, probability, work, centroids, and fluid pressure.
Prerequisites: Math 121.

201. Transition to Advanced Mathematics.
Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
A thorough introduction to the reading, writing, presenting and creating of mathematical proofs. Students will learn and practice in a careful and deliberate way the techniques used to prove mathematical theorems. Proofs studied will be chosen from a variety of fields such as set theory, number theory, analysis, algebra, and graph theory. Topics also include elements of the history and philosophy of mathematics and an introduction to the mathematical community.
Prerequisites: Math 122 or permission of instructor.

223. Calculus III.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
A continuation of Math 122: vector calculus, functions of several variables, partial derivatives, multiple integrals, line integrals, and Green’s theorem.
Prerequisites: Math 122.

251. Differential Equations.
Fall. Credits: 4.
Degree Requirements: Natural Science, F6.
The theory, methods, and applications of ordinary differential equations. Topics include existence, uniqueness and other properties of solutions, linear equations, power series and Laplace transform methods, systems of linear equations, and qualitative analysis.
Prerequisites: Math 122.

261. Linear Algebra.
Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
Topics include systems of linear equations, matrix algebra, determinants, real and complex vector spaces, linear transformations, eigenvalues and eigenvectors, and diagonalization. Attention is given to proofs.
Prerequisites: Math 122.

311-312. Mathematical Statistics and Probability.
Fall, Spring. Credits: 4-4.
Degree Requirements: Natural Science.
Topics include probability spaces, discrete and continuous random variables, independence, expectation, characteristic functions, the Central Limit Theorem, point and interval estimation, hypothesis testing, and regression. (Courses offered in alternate years; scheduled for 2009-2010.)
Corequisites: For 311, Math 223.
Prerequisites: For 312, Math 311.

321-322. Real Analysis.
Fall, Spring. Credits: 4-4.
Degree Requirements: Natural Science.
Topics include the real and complex number systems, metric spaces, sequences and series, continuity, and differentiation, as well as topics selected from the Riemann and the Riemann-Stieltjes integrals, sequences and series of functions, functions of several real variables, and Lebesgue theory. Emphasis is on careful proof. (Courses offered in alternate years; scheduled for 2008-2009.)
Prerequisites: For 321, Math 201 and Math 223. For 322, Math 321.

362-363. Abstract Algebra.
Fall, Spring. Credits: 4-4.
Degree Requirements: Natural Science.
An introduction to axiomatic algebraic structures. Topics include groups, subgroups, permutation groups, cyclic groups, normal subgroups, quotient groups, homomorphisms, isomorphisms, rings, integral domains, polynomial rings, ideals, quotient rings, fields, and extension fields. Additional topics may include finite fields, Galois theory, and advanced topics from linear algebra. (Courses offered in alternate years; scheduled for 2009-2010.)
Prerequisites: For 362, Math 201 and Math 261. For 363, Math 362.

370. Complex Variables.
Spring. Credits: 4.
Degree Requirements: Natural Science.
This course is an introduction to the theory of functions of a complex variable. Topics covered include complex numbers and their properties, analytic functions and the Cauchy-Riemann equations, complex logarithms, exponential and trigonometric functions, complex integration and the Cauchy integral formula, complex power series, the residue theorem, and applications to calculations of definite integrals. (Course offered every third year; scheduled for 2008-2009.)
Prerequisites: Math 223.

386. Junior Seminar.
Spring. Credits: 1.
This course will prepare students for the Senior Seminar experience. Students will attend the Senior Seminar presentations, pursue independent readings, and prepare a Senior Seminar prospectus for approval by the faculty of the department.

431. Topology.
Spring. Credits: 4.
Degree Requirements: Natural Science.
Topics selected from sets, functions, metric spaces, topological spaces, separation properties, compactness, connectedness, the Stone-Weierstrass theorem, mapping theorems, plane topology. (Course offered every third year; scheduled for 2010-2011.)
Prerequisites: Math 201 and Math 223.

455-456. Readings in Mathematics.
Fall, Spring. Credits: 1 to 4.
This course allows students to do advanced work not provided for in the regular courses. Its content will be fixed after consultation with the student and in accord with his or her particular interests.
Prerequisites: Permission of department chair.

460. Internship.
Fall, Spring. Credits: 1 to 4.
Internships in Mathematics and Computer Science, which are normally arranged by the Director of Career Services, are occasionally available and permit a qualified student to receive academic credit for off campus work experience. Internships are for Junior and Senior students majoring in the department. Subject to departmental approval, credit received may be used towards the major. Upon completion of the internship, the student makes written and oral reports focusing on an integration of the student’s academic work and the internship project. Interested students should contact the Chair of the department and the Director of Career Services.

465. Special Topics in Mathematics.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science.
An occasional offering of topics not covered in the existing mathematics courses. Topics may include but are not limited to: graph theory, Fourier analysis, measure theory, dynamical systems, foundations of mathematics, game theory, set theory, logic, non-Euclidean geometry, applied mathematics, and operations research.

482. Combinatorics.
Fall. Credits: 4.
Topics selected from basic counting principles, Ramsey theory, the inclusion/exclusion principle, recurrence relations, generating functions, partially ordered sets, systems of distinct representatives, combinatorial designs, graphs, directed graphs, partitions, combinatorial optimization, enumeration under group action, and an introduction to coding theory. (Course offered every third year; scheduled for 2009-2010.)
Prerequisites: Math 201 or permission of instructor.

485-486. Senior Seminar.
Fall, Spring. Credits: 1-2.
This course is meant to emphasize the unity and power of mathematics by applying and extending ideas drawn from courses required for all majors. Topics will be determined by a consultation among the students enrolled and the supervising faculty member. All participants will make several oral presentations.
Prerequisites: Math 261 or 223 and permission of supervisor.

495-496. Honors Tutorial in Mathematics.
Fall, Spring. Credits: 4 to 8.
Prerequisites: Permission of department chair.

COURSE OFFERINGS IN COMPUTER SCIENCE

103. Computer Information Fluency.
Fall. Credits: 4.
Degree Requirements: Natural Science, F6.
A broad introduction to computing appropriate for all students, regardless of intended major. This course introduces fundamentals of computers and computer information management primarily through projects that emphasize mastery of basic concepts, acquisition of skills, and logical reasoning. Concepts presented include computer data representation, an intro to architecture and how computers work, and basic network organization. Skills are developed to facilitate the use of a computer for communication and online research. Logical reasoning is fostered through working with models and abstraction, algorithmic thinking with an intro to programming, and critical evaluation of the use of computers and technology. Emphasis is on the development of a conceptual framework for further learning and problem-solving with computers, rather than on the use of specific software or hardware.

141. Computer Science I: Programming Fundamentals.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
An introduction to the fundamental concepts and practices of procedural programming. Topics include data types, control structures, functions, arrays, files, and the mechanics of running, testing, and debugging. Emphasis is placed on program design and problem solving techniques. The course also includes an introduction to the historical and social context of computing and an overview of computer science as a discipline.

142. Computer Science II: Object-Oriented Programming.
Spring. Credits: 4.
Degree Requirements: Natural Science, F6.
An introduction to the fundamental concepts and practices of object-oriented programming. The object-oriented programming paradigm is introduced, with a focus on the definition and use of classes as a basis for fundamental object-oriented program design. Other topics include an overview of programming language principles, simple analysis of algorithms, basic searching and sorting techniques, and an introduction to software engineering issues.
Prerequisites: Computer Science 141.

172. Discrete Structures for Computer Science.
Fall. Credits: 4.
Degree Requirements: Natural Science, F6.
An introduction to and survey of the mathematics used in computer science including functions, relations, sets, counting, logic, Boolean algebra, proof techniques, induction, recursion, computational complexity, and computability. Other topics may be included as time permits.
Prerequisites: Computer Science 141.

231. Introduction to Systems Programming and Computer Organization.
Spring. Credits: 4.
Degree Requirements: Natural Science.
A bottom-up exploration of the interaction between computer hardware and software. Topics include machine data representation and manipulation, binary file handling, addressing modes and dynamic memory allocation, an introduction to processes and threads, and process memory organization. Key layers of machine abstraction are illustrated through projects that involve an introduction to digital logic, assembly language programming, and an introduction to UNIX system programming.
Prerequisites: Computer Science 141.

241. Computer Science III: Data Structures and Algorithms.
Fall. Credits: 4.
Degree Requirements: Natural Science.
An introduction to the fundamental concepts of data structures and the algorithms that arise from them, using the object-oriented design paradigm. Data structures covered include stacks, queues, linked lists, hash tables, trees, and graphs. Other topics include an introduction to iterative and recursive algorithmic strategies and basic algorithm analysis.
Corequisite: Computer Science 172 (unless already taken).
Prerequisites: Computer Science 142.

315. Internet Programming.
Spring. Credits: 4.
Degree Requirements: Natural Science.
A survey of the special challenges encountered in the development of software for networked computing systems, including security, testing, maintenance, and reliability. Topics include the web as an example of client-server programming, the design and implementation of robust and maintainable web applications, use of multimedia technologies, designing for platform-independence, and programming ethics within the web community. 
Prerequisites: Computer Science 241.

320. Computer Graphics.
Spring. Credits: 4.
Degree Requirements: Natural Science.
Coverage of the basic concepts of 2D and 3D graphics, including an overview of graphics hardware, use of a graphics application programming interface, user interface design, techniques for computer animation, and graphical algorithms such as geometric transformations, clipping, windowing, hidden surface removal, and raster graphics techniques for the representation of curves, surfaces, and solids. (Course offered in alternate years; scheduled for 2007-2008.)
Corequisite: Math 223 or Math 261 (unless already taken).
Prerequisites: Computer Science 241.

330. Operating Systems.
Fall. Credits: 4.
Degree Requirements: Natural Science.
An introduction to the fundamentals of operating systems design and implementation. Topics include the process model and implementation of processes, an overview of the major components of a modern operating system, mutual exclusion and interprocess synchronization, a survey of scheduling algorithms, memory management techniques, and file systems. Examples are drawn from contemporary operating systems such as UNIX and Windows 2000. (Course offered in alternate years; scheduled for 2009-2010.)
Prerequisites: Computer Science 231.

335. Computer Architecture.
Fall. Credits: 4.
Degree Requirements: Natural Science.
An advanced study of the fundamental concepts in the design and organization of modern computer systems, focusing on how hardware has developed to support software requirements. Topics include a review of basic computer organization, instruction set design, processor design, memory system design, timing issues, interrupts, microcoding, and various performance-enhancing parallel techniques such as pipelining. Studies of existing architectures will illustrate how these design principles have been implemented. 
Prerequisites: Computer Science 231.

350. Theory of Computation.
Spring. Credits: 4.
Degree Requirements: Natural Science.
A study of theoretical models for computing. The hierarchy of finite state machines, pushdown machines, context free grammars, and Turing machines will be analyzed, along with their variations. The basic concepts of decidability, complexity theory, and NP-Complete problems will be introduced. 
Prerequisites: Computer Science 172.

355. Advanced Algorithms.
Spring. Credits: 4.
Degree Requirements: Natural Science.
An in-depth study of the design and analysis of advanced algorithms, including the performance tradeoffs and resources required by various algorithmic implementations. Major classes of computational problems will be identified and explored. Advanced data structures and approximation heuristics are introduced as required for solution design. Topics vary depending on the specific problems covered but will include the Master Theorem, dynamic programming, divide-and-conquer and greedy algorithms. (Course offered in alternate years; scheduled for 2009-2010.)
Prerequisites: Computer Science 241.

360. Programming Languages.
Spring. Credits: 4.
A wide-ranging and in-depth coverage of fundamental programming language concepts, presenting design issues of the various language constructs, and examining the design choices for these constructs in a range of the most popular contemporary programming languages. Language design alternatives are examined and critiqued. Methods of syntax description, common approaches to describing the semantics of programming languages, and various implementation approaches are covered. (Course offered in alternate years; scheduled for 2009-2010.)
Prerequisites: Computer Science 241.

455-456. Readings in Computer Science.
Fall, Spring. Credits: 1 to 4.
This course allows students to do advanced work not provided for in the regular courses. Its content will be fixed after consultation with the student and in accord with his or her particular interests.
Prerequisites: Permission of department chair.

460. Internship.
Fall, Spring. Credits: 1 to 4.
Internships in Mathematics and Computer Science, which are normally arranged by the Director of Career Services, are occasionally available and permit a qualified student to receive academic credit for off campus work experience. Internships are for Junior and Senior students majoring in the department. Subject to departmental approval, credit received may be used towards the major. Upon completion of the internship, the student makes written and oral reports focusing on an integration of the student’s academic work and the internship project. Interested students should contact the Chair of the department and the Director of Career Services.

465. Special Topics in Computer Science.
Fall, Spring. Credits: 4.
Degree Requirements: Natural Science.
An occasional offering of topics not covered in the existing computer science courses. Topics may include but are not limited to: Artificial Intelligence (search techniques, game playing, neural nets, machine learning); Database Systems (relational, hierarchical and network databases, security and synchronization); Operations Research (resource allocation and optimization techniques including linear programming, game theory, queueing theory and Markov chains).

485-486. Senior Seminar.
Fall, Spring. Credits: 1-4.
Fall term: This course lays the groundwork for the Spring Senior Seminar experience. Independent readings will be discussed and presented, and a Senior Seminar Project prospectus will be prepared and presented for approval by the faculty of the department. Spring term: This course comprises an in-depth exploration of the principles and techniques of analysis and design of software systems from an object-oriented perspective. Design patterns, a diagrammatic modeling language, and standard techniques of computer software specification, implementation, testing, and documentation will be explored and used as tools by students working in teams. Each team will produce a robust, scalable, and maintainable large-scale system based on the project proposal completed in CS 485. The Senior Seminar sequence is meant to emphasize the unity and power of computer science by applying and extending ideas drawn from the courses required for all Computer Science majors. All participants will make several oral presentations.
Prerequisites: Senior standing in the Computer Science major.

495-496. Honors Tutorial in Computer Science.
Fall, Spring. Credits: 4 to 8.
Prerequisites: Permission of department chair.