Mathematics and Computer Science

Associate Professors, Kontostathis, Neslen, Yahdi (Chair); Assistant Professor Dhawan, Hart, McGown, Scoville, Instructor Wait.

The Ursinus Mathematics and Computer Science Department offers majors in both mathematics and computer science. It also offers minors in computer science, mathematics, statistics, biostatistics and scientific computing. The mathematical sciences make significant contributions to society, engineering, medicine, physics, economics, and politics, and to other fields in the sciences and social sciences. The programs in the Mathematics and Computer Science Department provide students with the tools for analyzing and organizing data, as well as the theoretical underpinnings for modeling important and interesting concepts. These programs provide strong backgrounds in logical reasoning, excellent analytical skills, and the ability to learn new techniques and technologies. All of these attributes are sought after in current and emerging fields and careers.

The general aims of the department of mathematics and computer science are (1) to give the students a grasp of the ideas and methods of mathematics and computer science; (2) to develop an understanding and appreciation of mathematics as an abstract deductive system; (3) to give the students an appreciation of the historical importance of mathematics in the progress of civilization, both past and present; and (4) to provide the students with sufficient skills to enable them to apply their knowledge to related fields of study.

For students majoring in mathematics or computer science, the department aims to provide stimulation and preparation for (1) continued study at the graduate level; or (2) effective teaching in the secondary schools; or (3) employment in industrial research, statistics, computing, or actuarial positions. For other majors, it seeks to provide the mathematical competence required by the increasing quantitative emphasis in many of these disciplines.

Computer Science

Requirements for Majors

A student majoring in computer science is required to take CS-173, 174, 274, 275, 371; one of CS-373 or 374; CS-350; at least three other computer science courses at the 300- or 400-level, one of which must be a 400-level capstone course; MATH-236W; and one other course in mathematics or statistics numbered 112 or above, excluding STAT-140 and MATH/PHIL-260. Internships (CS-381, 382) and one-credit and two-credit research/independent work courses (CS-391, 392) do not fulfill any requirements for the major. Computer Science majors can fulfill the requirement for an oral presentation in the major by taking CS-350 and the capstone requirement by taking one of the following: CS-475, 476, 477, 478, or 492W.

While CS-394 always fulfills the ILE requirement for the college, CS-394 may satisfy an elective requirement for the major only with prior permission of the department chair.

Regardless of track, students must ensure that the major requirements are completed. The following tracks are intended to provide guidance for special career interests, not to substitute for the major requirements.

Track 1. Specialization in Software Engineering Students interested in software engineering should take CS-377, 474, either 476 or 477, and should complete at least one internship (CS-381 or 382).


Track 2. Specialization in Theoretical Computer Science Students interested in theoretical computer science should take CS-373, 374; MATH-235, 341, 361 and MATH-451/452 (Combinatorics). This track will be particularly useful for students who are interested in pursuing graduate study in computer science.


Track 3. Specialization in Game Design Students interested in working in the game industry should take CS-377, 476, 477; MATH-235, and should consider a minor in media studies or studio art.


Track 4. Specialization in Machine Learning Students interested in machine learning should take CS-377, 477; MATH/STAT-141Q, 242; MATH-235, 341, and independent study or independent research project in data mining is also recommended.


Track 5. Specialization in SystemsStudents interested in systems should take CS-376, 377, and 475.

Recommendations for Majors

Students are encouraged to elect either a minor in another discipline or additional courses in mathematics, statistics and computer science. The latter is especially recommended for students planning to do graduate work in the computer science or related discipline. Additional recommended mathematics courses are MATH-112, 211, 235, 310, 341 and 413, and MATH/STAT-141Q. Recommended ancillary courses are PHYS-111, 112, 209 and ECON-120.

Requirements for Minors

A minor concentration in computer science consists of CS-173, 174; and three additional courses chosen from MATH-236W, CS-274, 275, 371, 373, 374, 375, 376, 377, 471, 472, 474, 475, 476, 477.

Courses

CS-010. Computational Problem Solving Faculty

This workshop course offers a structured environment for helping students become better and more efficient computational problem-solvers. Focus is on the rapid development of software for solving hard problems. May be repeated for credit. Prerequisite: CS-173 or equivalent experience. Graded S/U. Three hours per week. One semester hour.

CS-170 Q. In Silico, Designing Simulations via Computer Science Dr. Dhawan

An introduction to computer science as a tool for analyzing and working with scientific data, and simulating experiments. The course introduces Python and studies its application in various scientific domains including Bioinformatics, Environmental Studies, Chemistry, Physics and Imaging by looking at a variety of problems drawn from these domains. The lab will involve the implementation of algorithms and analysis on data sets drawn from these areas. No prior programming experience is assumed. Offered every Fall. Three hours of lecture and two hours of laboratory per week. Four semester hours. (LS.)

Note: CS-170Q may not be used as elective credits for computer science majors or minors.

CS-173. Introduction to Computer Science Faculty

Introduction to the field of computer science. Topics include: methods for computational problem solving, algorithm development techniques, processes for development of new technologies, and programming projects of increasing complexity in a high-level language with emphasis on good programming style. The course also includes exposure to advanced topics in computer science such as graphics, human-computer interaction, and software engineering. Recommended for students in mathematics; business and economics; and the natural sciences. No prior computer programming experience is assumed. Offered every semester. Three hours of lecture and one hour of laboratory per week. Four semester hours.

CS-174. Object-Oriented Design Faculty

A continuation of CS-173. More detailed exploration of classes and instances, and an introduction to collection classes such as vectors, lists, maps and sets. Larger programs and/or team projects. Prerequisite: CS-173. Offered every semester. Three hours of lecture and one hour of lab per week. Four semester hours.

Note: Students who have taken CS-174 Data Structures can not take CS-174 Object-Oriented Design.

CS-274. Computer Architecture and Organization Faculty

Hierarchical structure of computer architecture, number systems, arithmetic operations, codes, switching algebra, logic gates, assembly language programming. Prerequisite: CS-174. Offered in the spring semester. Three hours of lecture and one hour of laboratory per week. Four semester hours.

CS-275. Software Engineering Dr. Kontostathis

Topics integral to the design, implementation and testing of a medium-scale software system combined with the practical experience of implementing such a project as a member of a programming team. Use of the Unified Modeling Language (UML) for software design. Prerequisite: CS-174. Offered in the fall semester. Three hours per week. Four semester hours.

CS-350. Oral Presentation Faculty

A computer science oral presentation. This course will satisfy the College requirement for an oral presentation in the major. Prerequisite: written consent of a department faculty member. Graded S/U. Zero semester hours.

Note: This course is usually taken in conjunction with internships (CS-381, 383) and research/independent work (CS-391-394, 491, 492).

CS-371. Data Structures and Algorithms Dr. Dhawan

Introduction to algorithm analysis and data structures. Complexity of algorithms, analyzing basic data structure operations, searching and sorting algorithms, tables, hashing, recursion, tree and graph algorithms. Prerequisites: MATH-111 or equivalent, MATH-236W, and CS-275, or permission of the instructor. Offered in the spring semester. Three hours per week. Four semester hours.

CS-373. Theory of Computation Dr. Dhawan

Principles of formal languages, automata, computability and computational complexity. Emphasis on writing proofs of theorems. Prerequisites: MATH-236W, CS-275. Offered in the fall of even years. Three hours per week. Four semester hours.

CS-374. Principles of Programming Languages Faculty

Syntax, processors, representations and styles of programming languages. Study and comparison of several modern programming languages. Prerequisite: CS-275. Offered in the spring of odd years. Three hours per week. Four semester hours.

CS-376. Operating Systems Faculty

Fundamental concepts of operating systems. Sequential processes, concurrent processes, resource management, scheduling, synchronization, file systems, and computer security. Projects include writing of a program to simulate major components of an operating system. Pre- or co-requisite: CS-274. Offered in the spring of even years. Three hours per week. Four semester hours.

CS-377. Database Design Dr. Kontostathis

The concepts involved in designing and using a database management system. Logical and physical database design. Entity-Relational Modeling. Various types of database structures, manipulations of a database structure through applications, query techniques, and programming in a database language. Prerequisite: CS-275. Offered in the fall of odd years. Three hours per week. Four semester hours.

CS-381. Internship Faculty

An off-campus academic/work experience under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 120 hours of work. Graded S/U. Prerequisites: three courses in computer science and approval of a faculty internship adviser. Three semester hours. (I.)

CS-382. Internship Faculty

An off-campus academic/work experience under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 160 hours of work. Graded S/U. Prerequisites: three courses in computer science and approval of a faculty internship adviser. Four semester hours. (I.)

Note: Students may receive credit for two internships that meet the conditions described in this catalogue.

CS-391. Research/Independent Work Faculty

Independent investigation of an area of computer science not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. One semester hour.

Note: This course may be taken more than once.

CS-392. Research/Independent Work Faculty

Independent investigation of an area of computer science not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. Two semester hours.

Note: This course may be taken more than once.

CS-394. Independent Study Faculty

Independent investigation of an area of computer science not covered in regular courses. Prerequisite: Written consent of a department faculty member. An oral presentation to the department is required. Four semester hours. (I.)

Note: This course may be taken more than once. This course always fulfills the ILE requirement for the college, but may satisfy an elective requirement for the major only with prior permission of the department chair

CS-471. Seminar in Computer Science I Faculty

A detailed study of an advanced topic in computer science, such as computational geometry, compilers, data mining, robotics or distributed technology. Prerequisites: CS-174 and written permission of the instructor. Usually offered in the fall semester of even years. May be repeated for credit. Three hours per week. Four semester hours.

CS-472. Seminar in Computer Science II Faculty

The course will cover topics similar to those listed in CS-471. Prerequisites: CS-174 and written permission of the instructor. Offered in the spring semester as needed. May be repeated for credit. Three hours per week. Four semester hours.

CS- 474. Human-Computer Interaction Dr. Dhawan

The study of human-computer interaction enables system architects to design useful, efficient, and enjoyable computer interfaces. This course teaches the theory, design procedure, and programming practices behind effective human interaction with computers. This course satisfies the College requirement for a capstone experience in the major. Prerequisite: CS-275. Offered in the spring semester of even years. Three hours per week. Four semester hours.

CS- 475. Computer Networks Faculty

Architecture and protocols of computer networks. Protocol layers; network topology; data-communication principles, including circuit switching, packet switching and error control techniques; sliding window protocols, protocol analysis and verification; routing and flow control; local and wide area networks; network interconnection; client-server interaction; emerging networking trends and technologies; topicsin security and privacy. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite or co-requisite: CS-274. Offered in the spring of odd years. Three hours per week. Four semester hours.

CS- 476. Computer Graphics Faculty

Software and hardware for interactive computer graphics. Implementation of device drivers, 3-D transformations, clipping, perspective, and input routines. Data structures, hidden surface removal, color shading techniques, and some additional topics will be covered. This course will satisfy the College requirement for a capstone experience in the major. Prerequisites: CS-275 and MATH-235. Offered fall of even years. Three hours per week. Four semester hours.

CS- 477. Artificial Intelligence Dr. Kontostathis

This course explores principles and methods for knowledge representation, reasoning, learning, problem solving, planning, heuristic search, and natural language processing. These principles are applied to problems which require building intelligent systems in a variety of domains. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: CS-275. Offered in fall of odd years. Three hours per week. Four semester hours.

CS-491. Research/Independent Work Faculty

Independent research in computer science. This course is appropriate for students pursuing departmental honors and distinguished honors projects, and is open to other students interested in research in computer science. An oral presentation to the department is required. Prerequisites: Written consent of a member of the faculty to serve as an advisor. Four semester hours. (I.)

Note: This course may be taken more than once.

CS-492W. Research/Independent Work Faculty

Independent research in computer science. This course serves as the culminating course for departmental honors and distinguished honors projects. This course will satisfy the college requirement for a capstone experience in the major. Prerequisites: CS-491, meets college and departmental requirements for honors, and written consent of a member of the faculty to serve as an advisor. Four semester hours. (I.)

Mathematics

Requirements for Majors

A student majoring in mathematics is required to take CS-173 and 40 credits in mathematics.

1. The following courses are required: CS-173 and Math-112, 211, 235, 236W, 311, 335, and 350.

2. In addition, one of the capstone courses is required: MATH-413, 421, 434, 442, or 492W.

3. The remaining 12 credits must be selected from 300-400-level mathematics courses, excluding internships (MATH-381, 382) and one credit and two credit research/independent work courses (MATH-391, 392).

Mathematics majors can fulfill the requirement for an oral presentation in the major by taking MATH-350.

While MATH-394 always fulfills the ILE requirement for the college, MATH-394 may satisfy an elective requirement for the major only with prior permission of the department chair. A student who is not prepared to take MATH-112 will need to take MATH-111.



Regardless of track, students must ensure that the major requirements are completed. The following tracks are intended to provide guidance for special career interests, not to substitute for the major requirements.

Track 1. Specialization in Pure Mathematics Students interested in Pure Mathematics should take MATH-312, 336, 411 and 421. This track will be particularly useful for students who are interested in pursuing graduate study in in pure mathematics or other theoretical fields.


Track 2. Specialization in Applied Mathematics Students interested in Applied Mathematics should take MATH-312, 413, 434 and 442. This track will be particularly useful for students who are interested in pursuing graduate study in all areas of applied mathematics and for students planning to seek jobs in industry or government. Additional courses in the sciences or social sciences are recommended.


Track 3. Specialization in Mathematics For Secondary Teaching Certificate Students preparing for secondary teaching must major in mathematics, and take MATH-322, 341, and 442 to satisfy the mathematics part of the certification requirements. In addition, the topic of the student’s MATH-350 oral presentation must be on some aspect of the history of mathematics. As many of the following as possible are strongly recommended: MATH-310, 434, and MATH/STAT-141Q, 242. If the student can take MATH/STAT-141Q and 242, they should be taken before MATH-341 and 442. Details may be obtained from the Mathematics and Computer Science Department or Education. Those students preparing for secondary teaching should consult the Ursinus College Education Department.


Track 4. Specialization in Actuarial Science Students with an interest in actuarial science are strongly encouraged to take MATH-211, 235, 342, 442; MATH-246 or STAT-240, 242; CS-173, 174. Due to the interdisciplinary nature of actuarial science, interested students are also encouraged to speak with departmental faculty early in their Ursinus career about the possibility of a student-initiated major in actuarial science and/or additional courses that may be relevant to actuarial science.

Recommendations for Majors

Students are encouraged to elect either a minor in another discipline or additional courses in mathematics, statistics and computer science. The latter is especially recommended for students planning to do graduate work in the mathematical sciences or related disciplines. ECON-120 and PHYS-111, 112, are recommended. Students planning to do postgraduate work in mathematics should take MATH-312 and 421. Students planning to seek jobs in industry should take MATH-310, 341, 413, and 442

PRE-ENGINEERING

Students interested in pursuing pre-engineering should contact the departmental chair at the earliest opportunity to plan a program of study.

Requirements for Minors in Mathematics

A minor concentration in mathematics consists of MATH-112, 211, 235; and two additional courses in mathematics chosen from MATH-236W, 310, 311, 312, 322, 335, 341, 413, 421, 434, 442, 451, 452.

Courses

MATH-010. Problem-Solving Faculty

A structured seminar, focusing on problem-solving. Students are encouraged to work collaboratively and individually on challenging mathematical problems that are presented without the context of techniques from a specific course. Problem-solving skills are enhanced, through using higher level thinking and applying techniques to different problem types. Problems in the fall semester include those from past Putnam exam while in the spring semester problems are drawn largely from professional journals. May be repeated for credit. Graded S/U. Three hours per week. One semester hour.

MATH-100. Mathematics for the Liberal Arts Faculty

A cultural and historical approach to mathematics. Appreciation of the beauty and creative aspects of mathematics and its role in nature and the arts. Essay tests and papers as well as problems using deductive reasoning. Offered in the spring semester. Three hours per week. Four semester hours. (M.)

MATH-110. Precalculus Faculty

A review of algebraic, exponential and logarithmic functions, Cartesian plane, circular, trigonometric and inverse trigonometric functions. Use of a computer algebra system. This course prepares students for MATH-111. Prerequisite: Placement based on the high school record and a placement test. Offered in the fall semester. Four hours per week. Four semester hours. (M.)

Note: A student who has received credit for MATH-105 or 111 may not enroll in MATH-110.

MATH-111. Calculus I Faculty

Limits; derivatives; applications of derivatives; trigonometric, inverse trigonometric, logarithmic, and exponential functions; applications of these functions; indeterminate forms; the Fundamental Theorem of Calculus. Use of a computer algebra system. Prerequisite: Placement based on the high school record and a placement test, or a grade of C- or better in MATH-110. Offered both semesters. Four hours per week. Four semester hours. (M.)

Note: A student who has received credit for MATH-111 may not enroll in MATH-110

MATH-112. Calculus II Faculty

A continuation of MATH-111.Techniques of integration, applications of integration, improper integrals, polar coordinates, parametric equations, infinite sequences and series. Use of a computer algebra system. Prerequisite: Placement based on the high school record and a placement test, or a grade of C- or better in MATH-111. Offered both semesters. Four hours per week. Four semester hours. (M.)

MATH-211. Multivariable Calculus Faculty

Functions of several variables, including three-dimensional geometry and vectors, space curves and motion in space, partial differentiation, multiple integration, line and surface integrals, and the theorems of Green, Gauss, and Stokes. Use of a computer algebra system. Prerequisite: A grade of C- or better in MATH-112, or permission of the department. Offered both semesters. Four hours per week. Four semester hours. (M.)

MATH-235. Linear Algebra Faculty

Systems of linear equations, matrix algebra, vector spaces, linear transformations, eigenvectors and eigenvalues, inner products and orthogonality, applications. The computer as a computational tool. Prerequisite: MATH-111 or equivalent, or permission of the instructor. Offered in the fall semester. Four hours per week. Four semester hours. (M.)

MATH-236W. Discrete Mathematics Dr.Scoville

A course designed to bridge the gap between computation-oriented introductory courses and proof-oriented advanced courses. The language of contemporary mathematics, including the proper way to write mathematics, and the nature of mathematical reasoning. Extensive writing projects. Topics studied may include axiomatic systems, logic, set theory, functions, mathematical induction, graph theory and trees, permutations and combinations. Prerequisite: MATH-111, or permission of the instructor. Offered in the spring semester. Three hours per week. Four semester hours. (M.)

MATH/PHIL-260. Logic Dr. Florka, Dr. Goetz

An introduction to the concepts and techniques used in symbolic reasoning, primarily through the study of first-order logic, the translation of sentences of ordinary English into a formal language, and the construction of derivations. Topics include: formalization, proofs, mathematical induction, propositional and predicate logic, quantifiers, and sets. (Formerly PHIL-202.) Three hours per week. Four semester hours. (M.)

Note: Students who have received credit for MATH-236W or the former PHIL-202 may not enroll in MATH/PHIL 260.

MATH-310. Differential Equations and Mathematical Models Dr. Yahdi

Mathematical methods for developing models in the physical, biological, and social sciences. Emphasis on models involving differential equations. Solutions, visualizations, and interpretations of first order, second order, and systems of linear and non-linear differential equations. Numerical, graphical and analytic methods, with extensive qualitative analysis approaches. Laplace transforms. Independent projects. Additional topics chosen from forcing and resonance, discrete dynamical systems, and power series solutions. Use of a computer algebra system. Prerequisite: MATH-112. Offered in the spring semester. Three hours per week. Four semester hours. (M.)

MATH-311. Analysis I Dr. Yahdi

An introduction to the real number system and set operations; theoretical treatment of supremum, infimum, countability, sequences, limits, continuity, and differentiability. Additional topics may include series, structure of point sets and abstract metric spaces. Emphasis on writing mathematical proofs. Prerequisite: MATH-211 and 236W. Offered in the fall semester. Three hours per week. Four semester hours. (M.)

MATH-312. Analysis II Dr. Yahdi

A continuation of MATH-311. The Riemann and Riemann-Stieltjes integral; infinite series, sequences and series of functions; introduction to metric spaces. Additional topics may include Lebesgue measure and integration, orthogonal functions and Fourier series. Prerequisite: MATH-311. Offered as needed.Three hours per week. Four semester hours. (M.)

MATH-322. Modern Geometry Dr. Scoville

Topics in Euclidean and non-Euclidean geometry, including some of the following: geometry from an axiomatic viewpoint, synthetic Euclidean geometry, transformation geometry and symmetry, affine and projective geometry, inversive geometry, spherical geometry, and hyperbolic geometry. Prerequisites: MATH-235 and 236W, or permission of the instructor. Offered in the spring of odd years. Three hours per week. Four semester hours. (M.)

MATH-335. Abstract Algebra Faculty

An introduction to algebraic structures, with emphasis on groups: Subgroups, quotient groups, homomorphisms, isomorphism theorems, Cayley’s theorem, permutation groups. Prerequisites: MATH-235 and 236W. Offered in the spring semester. Three hours per week. Four semester hours. (M.)

MATH-336. Abstract Algebra II Faculty

Alternating groups, simple groups, isomorphism theorems, series of groups, prime and maximal ideals, extension fields, automorphisms of fields, splitting fields, separable extensions, Galois theory, cyclotomic fields, insolvability of the quintic. Prerequisite: MATH-335. Offered in the fall of odd years. Three hours per week. Four semester hours. (M.)

MATH-341. Probability Dr. Hart

An introduction to probability theory, discrete and continuous probability distributions, moments and moment-generating functions of random variables, and transformations of random variables. Prerequisite: MATH-211. Offered in the fall semester. Four hours per week. Four semester hours. (M.)

MATH-350. Oral Presentation Faculty

A mathematics oral presentation. This course will satisfy the College requirement for an oral presentation in the major. Prerequisite: written consent of a department faculty member. Graded S/U. Zero semester hours.

Note: This course is usually taken in conjunction with internships (MATH-381, 383, 384, 441) and research/independent work (MATH-391-394, 441, 491, 492W).

MATH-361. Graph Theory Dr. Scoville

Elements of graph theory, including the study of Eulerian graphs, planar graphs, trees, connectivity, colorings, algorithms, domination, and the applications of graphs to computer science. Prerequisite: MATH-236W. Offered in the fall semester of even years. Three hours per week.Four semester hours.

MATH-381. Internship Faculty

An off-campus academic/work experience under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 120 hours of work. Graded S/U. Prerequisites: three courses in mathematics and approval of faculty internship adviser. Three semester hours. (I.)

MATH-382. Internship Faculty

An off-campus academic/work experience under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 160 hours of work. Graded S/U. Prerequisites: three courses in mathematics and approval of faculty internship adviser. Four semester hours. (I.)

Note: Students may receive credit for two internships that meet the conditions described in this catalogue.

MATH-391. Research/Independent Work Faculty

Independent investigation of an area of mathematics not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. One semester hour.

Note: This course may be taken more than once.

MATH-392. Research/Independent Work Faculty

Independent investigation of an area of mathematics not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. Two semester hours.

Note: This course may be taken more than once.

MATH-394. Independent Study Faculty

Independent investigation of an area of mathematics not covered in regular courses. An oral presentation to the department is required. Prerequisite: Written consent of a department faculty member. Four semester hours. (I.)

Note: This course may be taken more than once. This course always fulfills the ILE requirement for the college, but may satisfy an elective requirement for the major only with prior permission of the department chair.

MATH-411. Complex Analysis Faculty

Complex numbers; polar representation; stereographic projection; the exponential and logarithm functions; analytic functions; the Cauchy-Riemann Equations; fractional linear transformations; Cauchy’s integral formula; the theorems of Cauchy, Liouville, Morera, and Goursat; power series expansions; the Residue Theorem. Rouche's Theorem, the Schwartz Reflection Principle, and the Riemann Mapping Theorem." Prerequisite: MATH-236W and MATH-211. Offered in the spring semester of even years. Three hours per week. Four semester hours. (M.)

MATH-413. Numerical Analysis Dr. Yahdi

Selected topics from numerical analysis, which may include systems of linear equations, linear and nonlinear differential equations, numerical integration and differentiation, eigenvalue problems, error analysis, interpolation and approximation. The computer will be used. This course will satisfy the college requirement for a capstone experience in the major. Prerequisite: MATH-211. Offered in the fall semester of even years. Three hours per week. Four semester hours. (M.)

MATH-421. Topology Dr. Scoville

Elementary point set topology; metric spaces; topological spaces, quotient spaces, compactness, connectedness, and applications of topology to digital graphics, sensor networks, and robotics. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH- 236W. Offered in the spring semester of even years. Three hours per week. Four semester hours. (M.)

MATH-434. Number Theory Faculty 

Divisibility; factorization; distribution of primes; modular arithmetic; Diophantine equations; theorems of Fermat, Euler and Wilson; primitive roots; public-key cryptography, quadratic reciprocity. Additional topics may include: applications to cryptography; digital signatures; algebraic and transcendental numbers; continued fractions; elliptic curves. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH-236W. Offered in the fall semester of odd years. Three hours per week. Four semester hours. (M.)

MATH-442. Mathematical Statistics Faculty

The mathematical background of modern statistics, including the development of sampling distributions, the theory and application of estimation, tests of hypotheses. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH-341. Offered in the spring semester. Three hours per week. Four semester hours. (M.)

MATH-451. Topics in Advanced Mathematics I Faculty

A course designed to acquaint the student with modern trends in advanced topics in mathematics and its applications. The course will be adapted to the students’ preferences and needs. Prerequisite: Permission of the instructor. Three hours per week. Four semester hours. (M.)

MATH-452. Topics in Advanced Mathematics II Faculty

A course designed to acquaint the student with modern trends in advanced topics in mathematics and its applications. The course will be adapted to the student’s preferences and needs. Prerequisite: Permission of the instructor. Three hours per week. Four semester hours. (M.)

MATH-491. Research/Independent Work Faculty

Independent research in mathematics. This course is appropriate for students pursuing departmental honors and distinguished honors projects, and is open to other students interested in research in mathematics. An oral presentation to the department is required. Prerequisites: Written consent of a member of the faculty to serve as an advisor. Four semester hours. (I.)

Note: This course may be taken more than once.

MATH-492W. Research/Independent Work Faculty

Independent research in mathematics. This course serves as the culminating course for departmental honors and distinguished honors projects. This course will satisfy the college requirement for a capstone experience in the major. Prerequisites: MATH-491, meets college and departmental requirements for honors, and written consent of a member of the faculty to serve as an advisor. Four semester hours. (I.)

STATISTICS

Requirements for Minors in Statistics

A minor concentration in statistics consists of MATH/STAT-141Q, STAT-240 (or MATH-246), 242 or 243W; and two additional courses selected from among MATH-341, 442; STAT-342, 382, 441, 451; or 4 credit hours of independent study/research consisting of any combination of STAT-391, 392, and 394.

Requirements for Minors in Biostatistics

A minor concentration in biostatistics consists of one course in an area of application selected from among: BIO-101Q, 102Q; NEURO-120Q; PSYC-100; HEP-100, or ENV-100; MATH/STAT-141Q, STAT-240 (or MATH-246) , 243W; and one course selected from among STAT-342, 384 or 441.

Courses

STAT-140Q. Statistical Reasoning Faculty

A study of the role of statistics in a wide variety of academic fields and in everyday life. This course is intended for students who want an appreciation of statistics, but do not imagine that they will ever need to carry out statistical analyses themselves. Emphasis is placed on the ability to interpret and critically evaluate statistical claims. Offered both semesters. Three hours per week. Four semester hours (M.).

Note: This course cannot be counted toward a major or a minor in mathematics, a minor in statistics, or a minor in biostatistics. It is not a prerequisite for any other course. It cannot be taken for credit after or concurrently with any other statistics course, including AP Statistics.

STAT-141Q. Statistics I Faculty

A study of the fundamental concepts of statistical analysis. This course prepares students to carry out basic descriptive and inferential statistical analyses with the aid of computer software. Topics include an introduction to the nature of statistical reasoning, graphical and descriptive statistics, and design of experiments, sampling methods, probability, probability distributions, sampling distributions, and statistical inference based on confidence intervals and hypothesis tests. Examples will be drawn from a wide variety of disciplines. Offered both semesters. Four hours per week. Four semester hours. (M.)

Note: MATH-241Q, MATH/STAT-242 or MATH/STAT-442 may not enroll in MATH/STAT-141Q.

STAT-242 Statistics II Faculty

A continued study of basic statistical techniques. Topics include: regression analysis, chi-square tests, nonparametric statistics, and the use of statistical software for data analysis. Prerequisite: MATH/STAT-141Q or MATH/STAT-442; STAT-240 or MATH-246. Offered in the spring semester. Four hours per week.  Four semester hours. (M.)

STAT-243W Biostatistics Dr. Hart

A study of inferential statistical techniques appropriate to the biological sciences. This course employs a case-study approach in which students use statistical software to examine real world data. Students will be required to produce statistical reports summarizing their statistical methods and results. Prerequisites: MATH/STAT-141Q or MATH/STAT-442; STAT-240 or MATH-246. Offered in the fall semester. Four hours per week. Four semester hours. (M.)

Note: Students may not receive credit for both MATH/STAT-242 and MATH/STAT-243W.

STAT-240. Computational Statistics (SAS)Faculty

Statistical analysis using statistical software. Design, collection, organization, and storage of data sets. Statistical programming, debugging, analysis of output and interpretation of results. Prerequisite: MATH/STAT-141Q. Offered in the spring semester. Four hours per week. Four semester hours.

Note: STAT-240 does not fulfill the College Core Mathematics requirement.

STAT-342. Applied Regression Models Faculty

A study of regression models. This course will begin by considering the matrix approach to simple linear regression and progress to more general modeling approaches including multiple regression models and analysis of variance (ANOVA). Models, inferences, diagnostics, and remedial measures for dealing with invalid assumptions will be examined. Prerequisites: MATH/STAT-242 or 243W; MATH-235 or permission of instructor. Offered in the spring semester. Three hours per week. Four semester hours. (M.)

STAT-382. Internship Faculty

An off-campus academic/work experience related to statistics conducted under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 160 hours of work. Graded S/U. Prerequisites: MATH/STAT-242 or 243(W), and approval of a faculty internship adviser. Four semester hours. (I.)

STAT-384. Internship in BiostatisticsFaculty

An off-campus academic/work experience related to statistics conducted under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 160 hours of work. Graded S/U. Prerequisites: MATH/STAT-242 or 243(W), and approval of a faculty internship adviser. Four semester hours. (I.)

STAT-392. Research/Independent WorkFaculty

Independent investigation of an area of statistics not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. Two semester hours.

Note: This course may be taken more than once.

STAT-394. Independent StudyFaculty

Independent investigation of an area of statistics not covered in regular courses. An oral presentation to the department is required. Prerequisite: Written consent of a department faculty member. Four semester hours. (I.)

Note: This course may be taken more than once. This course always fulfills the ILE requirement for the college, but may satisfy an elective requirement for the major only with prior permission of the department chair.

STAT-441W. Applied Research Seminar in BiostatisticsDr. Hart

A study of current problems in biostatistics. The course will introduce students to fundamental research procedures and data analysis. Students will work independently on a research problem of their choosing. Each student will be required to present on their progress throughout the semester and produce a culminating statistical report on their project. Students should expect to spend at least 12 hours per week working on their research project. Prerequisites: MATH/STAT-242 or MATH/STAT-243W and written permission of a department faculty member required. Four semester hours. (M.)

STAT-451. Topics in Advanced StatisticsFaculty

A course designed to acquaint students with advanced topics in statistics and its applications. The course will be adapted to students’ preference and needs. Prerequisite: Permission of the instructor. Three hours per week. Four semester hours. (M.)

SCIENTIFIC COMPUTING

Modeling, computational, quantitative and numerical methods are increasingly important and widely employed in STEM fields for simulation, experimentation, analysis, and design. The interdisciplinary scientific computing minor provides students in the sciences and the mathematical sciences with opportunities to be knowledgeable across a broad range of disciplines, capable of communicating well with researchers in other disciplines, and cognizant of emerging roles of computational techniques.

Requirements for Minors in Scientific Computing

A minor concentration in scientific computing consists of six courses (24 credits). No more than three courses with the same prefix may count towards the minor, no more than three courses may count toward any other single major or minor, and no more than three courses can be taken at or lower than the 200-level.

  • Core Courses (8 credits): CS-174 and MATH-310.
  • Elective Courses (16 credits): Four electives chosen from the following list: BCMB-307, BCMB/BIO-429W; BIO/ENV-250, 415; CHEM-212, 309, 310, 410W; CS-371, 373, 476; ENV-370, 372; HEP-352Q; MATH-235, 413; MATH-246 or STAT-240, 243, 342; NEUR-120Q, NEUR/PSYC-335, NEUR/BIO-431, 435; PHYS-122, 299, 316, 405, 408W.

An ILE with a component related to the minor topics is strongly recommended.