Mathematics, Computer Science and Statistics
Faculty

Professor Scoville (Chair); Associate Professors Mongan, Sadowski; Assistant Professors Kozhushkina, MontesinosYufa, New, Takyi, Tralie; Assistant Professors, Instructors Grossbauer and Veca Schilling; Instructor, Visiting Adam.

The Ursinus Department of Mathematics, Computer Science, and Statistics offers majors in both mathematics, computer science, and statistics. 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 Department of Mathematics, Computer Science, and Statistics 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.
For students majoring in mathematics, computer science, or statistics, the department aims to provide preparation for (1) continued study at the graduate level; or (2) effective teaching in the secondary schools; or (3) employment in business, industry, statistics, computing, or actuarial sciences. For other majors, it seeks to provide the mathematical competence required by the increasing quantitative and analytical emphasis required in many disciplines and careers.
Computer Science
Upon graduation students majoring in computer science should be able to:
 Engineer multiplecomponent systems that solve realworld problems
 Program, test and debug in a variety of languages
 Learn new technologies and tools on their own
 Design, implement and analyze algorithms and data structures
 Describe the concept of computability
 Communicate to technical and nontechnical audiences, verbally and in writing
 Work independently and in groups
 Articulate the social and ethical issues pertaining to the creation and use of technology
Requirements for Majors
A student majoring in computer science is required to take:
 CS173, 174, 271, 274
 CS373 or 374
 CS375
 CS350 or MATH350
 At least three other computer science courses at the 300 or 400level, one of which must be a 400level capstone course
 MATH236W
 One other course in mathematics numbered 112 or above, excluding MATH/PHIL260.
Internships (CS381, 382) and onecredit and twocredit research/independent work courses (CS391392) do not fulfill any requirements for the major. Computer Science majors can fulfill the requirement for an oral presentation in the major by taking CS350 or MATH350 and the capstone requirement by taking one of the following: CS474, 475, 476, 477, or 492W.
While CS394 always fulfills the ILE requirement for the college, CS394 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 CS377, 474, either 476 or 477, and should complete at least one internship (CS381 or 382).
Track 2. Specialization in Theoretical Computer Science Students interested in theoretical computer science should take CS373, 374; MATH235, 341, and 361. 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 CS377, 476, 477; MATH235, 361; DIGS250; and should consider a minor in media studies or studio art.
Track 4. Specialization in Machine Learning Students interested in machine learning should take CS372, 377, 477; STAT141Q, 242; MATH235, 341, 361; and independent study or independent research project in data mining is also recommended.
Track 5. Specialization in Systems Students interested in systems should take CS376, 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 computer science or related disciplines. Additional recommended mathematics courses are MATH112, 211, 235, 310, 341, 361 and 413, and STAT141Q. Recommended ancillary courses are PHYS111, 112, and introductory and intermediatelevel economics courses.
Requirements for Minors
A minor in computer science consists of CS173, 174; and three additional courses chosen from MATH236W, CS271, 274, 372, 373, 374, 376, 377, 471, 472, 474, 475, 476, 477.
Mathematics
Requirements for Majors
Upon graduation students majoring in mathematics should be able to:
 Organize and synthesize evidence to identify patterns and formulate conjectures
 Demonstrate mastery of the standard proof techniques
 Solve problems with mathematical components, and use standard software packages when appropriate
 Communicate to technical and nontechnical audiences, verbally and in writing
 Work independently and in groups
 Articulate the importance of mathematical and analytical reasoning as a fundamental skill that is one of the hallmarks of a liberal education
A student majoring in mathematics is required to take:
 MATH112, 211, 235, 236W, 311, and 335
 CS350 or MATH350
 At least four other mathematics courses at the 300 or 400level, one of which must be a 400level capstone course. MATH400 does not count as an elective towards the math major.
 CS173
Internships (MATH381, 382), onecredit and twocredit research/independent work courses (MATH391392), and MATH400 do not fulfill any requirements for the major. Mathematics majors fulfill the requirement for an oral presentation in the major by taking MATH350 or CS350 and the capstone requirement by taking one of the following: MATH413, 421, 434, 442 or 492W.
While MATH394 always fulfills the ILE requirement for the college, MATH394 may satisfy an elective requirement for the major only with prior permission of the department chair. A student who is not prepared to take MATH112 will need to take MATH111.
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 MATH312, 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 MATH312, 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. Requirements for Students Pursuing Teaching Certification in Mathematics Students preparing for secondary teaching must major in mathematics, and take MATH322, 341, and 442 to satisfy the mathematics part of the certification requirements. In addition, the topic of the student’s MATH350 oral presentation must be on some aspect of the history of mathematics. As many of the following as possible are strongly recommended: MATH310, 434, and STAT141Q, 242. If the student can take STAT141Q and 242, they should be taken before MATH341 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. There is both a departmental and college minimum GPA requirement for student teaching.PreEngineering
Students interested in pursuing preengineering should contact the departmental chair at the earliest opportunity to plan a program of study.
Actuarial Science
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 studentinitiated major in actuarial science and/or additional courses that may be relevant to actuarial science. 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 MATH312, 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 MATH310, 341, 361, 413, 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, as is minoring in computer science and/or statistics.Track 3. Specialization in Business and Industry
Students interested in entering the workforce immediately upon graduation should consider taking: CS174, CS375, STAT141Q, MATH310, 341, 442 as well as courses offered in the Business and Economics and the Media and Communication studies departments. A management studies minor is strongly recommended.Recommendations for Majors
Students are encouraged to elect either a minor in another discipline or additional courses in mathematics, statistics and computer science. PHYS111 and 112, are recommended.
Requirements for Minors in Mathematics
A minor in mathematics consists of MATH112, 211, 235; and two additional courses in mathematics chosen from MATH236W, 310, 311, 312, 322, 335, 341, 361, 411, 413, 421, 434, 442, 451, 452.
Statistics
Requirements for Majors in Statistics
A student majoring in statistics is required to take:
 MATH112
 STAT141
 STAT142
 MATH211
 MATH235
 STAT240 or DATA/STAT150
 STAT242W or STAT243W
 MATH341
 STAT342
 STAT 350, CS350 or MATH350
 MATH442
 STAT443W
 At least two of the following: MATH311, MATH/STAT343, STAT 244, STAT444, CS377, CS477, ECON300Q
Internships (STAT381, 382) and onecredit and twocredit research/independent work courses (STAT391392) do not fulfill any requirements for the major. Statistics majors can fulfill the requirement for an oral presentation in the major by taking STAT350, CS350, or MATH350 and the capstone requirement by taking STAT443W.
While STAT394 always fulfills the XLP requirement for the college, STAT394 may satisfy an elective requirement for the major only with prior permission of the department chair.Requirements for Minors in Statistics
A minor concentration in statistics consists of:
 STAT141Q, 142, 240
 STAT242W or 243W
 Two additional courses selected from among MATH341, 442; DATA/STAT150, STAT244, 342, 343, 382, 441, 451; or 4 credit hours of independent study/research consisting of any combination of STAT391, 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 BIO101Q, 102Q; PSYC100; HEP100; or ENV100
 STAT141Q, 142, 240, 243W
 one course selected from among STAT342, 384, or 441.
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 200level.
 Core Courses (8 credits): CS174 and MATH310.
 Elective Courses (16 credits): Four electives chosen from the following list: BCMB307, BCMB/BIO429W; BIO/ENV415; CHEM309, 310, 315, CS373, 476; ENV370, 372; HEP352Q; MATH235, 413; STAT240, 243W, 342; NEUR/BIO431W, 435W; PHYS122Q, 299, 301, 304, 305, 306, 328W, 329W, 338W, 339W, 401, 409, 410, 491.
An ILE with a component related to the minor topics is strongly recommended.
Courses

Computer Science
CS010. Computational Problem Solving
This workshop course offers a structured environment for helping students become better and more efficient computational problemsolvers. Focus is on the rapid development of software for solving hard problems. May be repeated for credit. Prerequisite: CS173 or equivalent experience. Graded S/U. Three hours per week. One semester hour.
CS170Q. Programming for the World around Us
An introduction to programming and computer science as a tool for solving problems, automating work, and analyzing and working with data. The course introduces Python and studies its applications in various domains including bioinformatics, the physical sciences, business, and humanities 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. Also, the ethics of data use are covered via discussion of relevant articles and media. No prior programming experience is assumed. Offered every Fall. Three hours of lecture and one hour of laboratory per week. Four semester hours. (R, S.)
Note: CS170Q may not be used as elective credits for computer science majors or minors. It cannot be taken for credit after or concurrently with any other computer science course, including AP Computer science.
.CS173. Introduction to Computer Science
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 highlevel language with emphasis on good programming style. The course also includes exposure to advanced topics in computer science such as graphics, humancomputer 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. (Q, R.)
CS174. ObjectOriented Programming
A continuation of CS173. More detailed exploration of classes and instances. An introduction to collection classes such as vectors, arraylists, linked lists, stacks, queues, maps, sets, and trees. Larger programs and/or team projects. Prerequisite: A grade of C– or higher in CS173. Offered every semester. Three hours of lecture and one hour of lab per week. Four semester hours. (R.)
CS271. Data Structures and Algorithms
Introduction to algorithm analysis and data structures. Complexity of algorithms, analyzing basic data structure operations, searching and sorting algorithms, tables, hashing, recursion, dynamic programming, tree and graph algorithms. Prerequisites: MATH111 or equivalent and a grade of C– or higher in CS174, or permission of the instructor. Offered in the fall semester. Three hours per week. Four semester hours.
Note: Students who completed CS371W can not enroll in CS271.
CS274. Computer Architecture and Organization
Hierarchical structure of computer architecture, number systems, arithmetic operations, codes, switching algebra, logic gates, assembly language programming. Prerequisite: CS174. Offered in the spring semester. Three hours of lecture and one hour of laboratory per week. Four semester hours.
CS350. Oral Presentation
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 (CS381, 383) and research/independent work (CS391394, 491, 492).
CS372. Digital Musical Audio Processing
This handson course will take a broad overview of how to represent, analyze, and morph/transform digital musical audio with a computer. Topics include timedomain audio processing, digital instrument synthesis (including FM synthesis), frequency domain audio processing and Fourier analysis, vocoders and crosssynthesis, audio novelty for tempo estimation / beattracking, pitch and timbre features, contentbased music audio retrieval (e.g., version identification and the “Shazam algorithm”), automatic source separation, and audio mosaicing. Prerequisite: MATH111 and CS174 (or CS173 with permission of the instructor). Offered in spring of odd years. Three hours per week. Four semester hours.
CS373. Theory of Computation
Formal introduction to the limits of computation using mathematical models of computation. Topics include finite state automata, the pumping lemma, context free grammars, pushdown automata, Turing machines, recognizability and decidability, computational complexity, and the CookLevin theorem. Emphasis on writing proofs of theorems. Prerequisites: MATH236W, a grade of C– or higher in CS174. Offered in the fall of odd years. Three hours per week. Four semester hours.
CS374. Principles of Programming Languages
Syntax, processors, representations and styles of programming languages. Study and comparison of several modern programming languages. Prerequisite: A grade of C– or higher in CS174. Offered in the fall of even years. Three hours per week. Four semester hours.
CS375. Software Engineering
Topics integral to the design, implementation and testing of a mediumscale 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: A grade of C– or higher in CS271. Offered in the spring semester. Three hours per week. Four semester hours. (Q.)
Note: Students who completed CS275 cannot enroll in CS375.
CS376. Operating Systems
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 corequisite: CS274. Offered in the spring of even years. Three hours per week. Four semester hours.
CS377. Database Design
The concepts involved in designing and using a database management system. Logical and physical database design. EntityRelational Modeling. Various types of database structures, manipulations of a database structure through applications, query techniques, and programming in a database language. Prerequisite: CS271. Offered in the fall of odd years. Three hours per week. Four semester hours.
CS381. Internship
An academic/work experience under the supervision of an internship adviser and an onsite supervisor. Students must document their experience according to the requirements delineated in the College catalogue section on Internships. 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. (XLP.)
CS382. Internship
An academic/work experience under the supervision of an internship adviser and an onsite supervisor. Students must document their experience according to the requirements delineated in the College catalogue section on Internships. 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. (XLP.)
Note: Students may receive credit for two internships that meet the conditions described in this catalogue.
CS391. Research/Independent Work
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.
CS392. Research/Independent Work
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.
CS394. Independent Study
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. (XLP.)
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
CS471. Seminar in Computer Science I
A detailed study of an advanced topic in computer science, such as computational geometry, compilers, data mining, robotics or distributed technology. Prerequisites: CS271 or 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.
CS472. Seminar in Computer Science II
The course will cover topics similar to those listed in CS471. Prerequisites: CS271 or 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. HumanComputer Interaction
The study of humancomputer 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: CS375. Offered in the spring semester of even years. Three hours per week. Four semester hours.
CS475. Computer Networks
Architecture and protocols of computer networks. Protocol layers; network topology; datacommunication 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; clientserver 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 corequisite: CS274. Offered in the spring of odd years. Three hours per week. Four semester hours.
CS476. Computer Graphics
A broad introduction to computer graphics via study and implementation of algorithms for 3D rendering, 3D shape manipulation, and 3D animation. Rendering topics include geometric primitives, scene graphs, 3D perspectives, ray tracing, the objectfirst graphics pipeline (including projection, clipping, shading, hidden surface removal, and displacement maps), antialiasing, texture maps, shadows, specular reflection, and global illumination. Shape manipulation topics include data structures for 2D surfaces (triangle meshes, subdivision surfaces, splines) and volumetric/levelset data structures (implicit surfaces). Animation topics include rotation interpolation, rigging/skinning, and particle/spring simulations. Students will also learn realtime software implementations of shading via the OpenGL Shading Language (GLSL). Prerequisites: CS271 or 274. Offered fall of even years. Three hours per week. Four semester hours. (LINQ if concurrently enrolled in DIGS250).
CS477. Artificial Intelligence
This course explores principles and methods for knowledge representation, reasoning, learning, problem solving, planning, heuristic search, multimedia data processing, and natural language processing. These principles are applied to problems which require building intelligent systems in a variety of domains. Ethical considerations in developing responsible AI will also be explored. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH111; CS271 or 274. Offered in fall of odd years. Three hours per week. Four semester hours. (O.)
CS491. Research/Independent Work
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. (XLP.)
Note: This course may be taken more than once.
CS492W. Research/Independent Work
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: CS491, meets college and departmental requirements for honors, and written consent of a member of the faculty to serve as an advisor. Four semester hours. (XLP.)
Mathematics
MATH010. ProblemSolving
A structured seminar, focusing on problemsolving. Students are encouraged to work collaboratively and individually on challenging mathematical problems that are presented without the context of techniques from a specific course. Problemsolving 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.
MATH110. Precalculus
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 MATH111. Prerequisite: Placement based on the high school record and a placement test. Offered in the fall semester. Four hours per week. Four semester hours. (R.)
Note: A student who has received credit for MATH105 or 111 may not enroll in MATH110.
MATH111. Calculus I
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 MATH110. Offered both semesters. Four hours per week. Four semester hours. (Q, R.)
Note: A student who has received credit for MATH111 may not enroll in MATH110
MATH112. Calculus II
A continuation of MATH111.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 MATH111. Offered both semesters. Four hours per week. Four semester hours. (Q, R.)
MATH211. Multivariable Calculus
Functions of several variables, including threedimensional 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 MATH112, or permission of the department. Offered both semesters. Four hours per week. Four semester hours. (Q, R.)
MATH235. Linear Algebra
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: MATH112 or 236W, or permission of the instructor. Offered in the fall semester. Four hours per week. Four semester hours. (R.)
MATH236W. Discrete Mathematics
A course designed to bridge the gap between computationoriented introductory courses and prooforiented 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: MATH111, placement or permission of the instructor. Offered in the spring semester. Three hours per week. Four semester hours. (R.)
MATH/PHIL260. Logic
An introduction to the concepts and techniques used in symbolic reasoning, primarily through the study of firstorder 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 PHIL202.) Three hours per week. Four semester hours. (R.)
Note: Students who have received credit for MATH236W or the former PHIL202 may not enroll in MATH/PHIL260.
MATH310. Differential Equations and Mathematical Models
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 nonlinear 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: MATH211 and 235. Offered in the spring semester. Three hours per week. Four semester hours.
MATH311W. Analysis I
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: MATH211 and 236W. Offered in the fall semester. Three hours per week. Four semester hours.
MATH312. Analysis II
A continuation of MATH311. The Riemann and RiemannStieltjes 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: MATH311. Offered as needed.Three hours per week. Four semester hours. (R.)
MATH322. Modern Geometry
Topics in Euclidean and nonEuclidean 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: MATH235 and 236W, or permission of the instructor. Offered in the spring of odd years. Three hours per week. Four semester hours. (R.)
MATH335. Abstract Algebra
An introduction to algebraic structures, with emphasis on groups: Subgroups, quotient groups, homomorphisms, isomorphism theorems, Cayley’s theorem, permutation groups. An introduction to the theory of rings. Additional topics may include: series of groups, free groups, and the Sylow theorems. Prerequisites: MATH235 and 236W. Offered in the spring semester. Three hours per week. Four semester hours.
MATH336. Abstract Algebra II
An introduction to algebraic structures, with emphasis on rings: subrings, ideals, quotient rings, homomorphisms, isomorphism theorems, integral domains, unique factorization domains, Euclidean domains. Additional topics may include: fields and field extensions, Galois theory. Prerequisite: MATH335. Offered in the fall of odd years. Three hours per week. Four semester hours. (R.)
MATH341. Probability
An introduction to probability theory, discrete and continuous probability distributions, moments and momentgenerating functions of random variables, and transformations of random variables. Prerequisite: MATH211. Offered in the fall semester. Four hours per week. Four semester hours.
MATH/STAT343. Math for Data
An introduction to the mathematical foundations of computational data analysis. The course will explore several core topics including Bayes rule, principal component analysis and dimensionality reduction, gradient descent, classification and clustering, and graphs as models. Offered in the fall of odd years. Prerequisites: Math 235 and Math 341 or permission of instructor. 3 hours per week. Four semester hours.
MATH350. Oral Presentation
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 (MATH381, 383, 384, 441) and research/independent work (MATH391394, 441, 491, 492W).
MATH361. Graph Theory
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: MATH236W. Offered in the fall semester of even years. Three hours per week. Four semester hours.
MATH381. Internship
An academic/work experience under the supervision of an internship adviser and an onsite supervisor. Students must document their experience according to the requirements delineated in the College catalogue section on Internships. 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. (XLP.)
MATH382. Internship
An academic/work experience under the supervision of an internship adviser and an onsite supervisor. Students must document their experience according to the requirements delineated in the College catalogue section on Internships. 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. (XLP.)
Note: Students may receive credit for two internships that meet the conditions described in this catalogue.
MATH391. Research/Independent Work
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.
MATH392. Research/Independent Work
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.
MATH394. Independent Study
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. (XLP.)
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.
MATH400. Mathematics for Human Flourishing
Many people today consider mathematics a tool of the physical sciences at best and a pointless exercise in rote memorization at worst. But is there anything more to math than this? Can mathematics contribute to basic human desires such as play, beauty, freedom, justice, and love? Is there any sense in which mathematics can contribute to human flourishing? How does our view of the nature of mathematics affect things like education, personal growth, and human flourishing? This course explores ways in which mathematics can be linked to what it means to be human. Through a series of readings, both ancient and modern, covering history, philosophy, logic, and personal anecdotes, this course challenges our assumptions about how mathematics fits into the modern world and how mathematics calls us to action, even the most mathphobic. Offered in the fall semester. Three hours per week. Four semester hours. (CCAP.)
Note: MATH400 does not count as an elective towards the math major or minor. The course does not count towards the (R) college core requirement.
MATH411. Complex Numbers
Complex numbers; polar representation; stereographic projection; the exponential and logarithm functions; analytic functions; the CauchyRiemann 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. Prerequisites: MATH236W and 211. Offered in the spring semester of even years. Three hours per week. Four semester hours.
MATH413. Numerical Analysis
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: MATH211. Offered in the fall semester of even years. Three hours per week. Four semester hours. (R.)
MATH421. Topology
Elementary point set topology; metric spaces; topological spaces, quotient spaces, compactness, and connectedness. Additional topics may include homology or the fundamental group. 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.
MATH434. Number Theory
Divisibility; factorization; distribution of primes; modular arithmetic; Diophantine equations; theorems of Fermat, Euler and Wilson; primitive roots; publickey 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: MATH236W. Offered in the fall semester of odd years. Three hours per week. Four semester hours.
MATH442. Mathematical Statistics
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: MATH341. Offered in the spring semester. Three hours per week. Four semester hours.
MATH451. Topics in Advanced Mathematics I
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. (R.)
MATH452. Topics in Advanced Mathematics II
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. (R.)
MATH491. Research/Independent Work
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. (XLP.)
Note: This course may be taken more than once.
MATH492W. Research/Independent Work
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: MATH491, meets college and departmental requirements for honors, and written consent of a member of the faculty to serve as an advisor. Four semester hours. (XLP.)
Statistics
STAT140Q. Statistical Reasoning
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 (R.).
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.
STAT141Q. Statistics I
A study of the fundamental concepts of statistical analysis using a simulation based approach in addition to the traditional theory based approach. 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. (R.)
Note: This course cannot be counted toward a major or a minor in mathematics. It cannot be taken for credit after or concurrently with any other statistics course, including AP Statistics.
STAT142. R Lab
Introduction to the use of computer program R to implement basic statistical techniques. Topics include: graphics, correlation, ttests, significance testing for proportions and regression. Students pursuing a statistics major or minor should take this concurrently with STAT141Q. Offered every semester. One hour per week. One semester hour.
STAT/DATA150. R for Data Science
A handson study of the statistical programming language R for liberal arts students. This course prepares students to collect, manipulate, analyze, and visualize realworld data using R with a focus on data science applications. A final project will consist of analyzing and visualizing CIE readings statistically. Key R packages to use include (and will not be limited to) base, readr, readxl, stringr, knitr, dplyr, dbplyr, lubridate, ggplot2, tidytext, mlr3, caret, rmarkdown, datatable, and the tidyverse suite. Examples will be drawn from various disciplines centered on students’ interests. Offered in Spring. Prerequisites: STAT142 and either CIE100 or CIE150 or CIE200, or permission from the instructor. Four hours per week. Four semester hours.
STAT240. Computational Statistics (SAS)
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/STAT141Q. Offered in the spring semester. Four hours per week. Four semester hours.
Note: STAT240 does not fulfill the College Core Mathematics requirement.
STAT242W Statistics II
A continued study of basic statistical techniques. Topics include: regression analysis, chisquare tests, nonparametric statistics, and the use of statistical software for data analysis. Prerequisite: STAT142 and STAT141Q or MATH442. Offered in the spring semester. Four hours per week.
Students may not receive credit for both STAT242W and STAT243W
STAT243W Biostatistics
A study of inferential statistical techniques appropriate to the biological sciences. This course employs a casestudy 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: STAT141Q and STAT142. Offered in the fall semester. Four hours per week. Four semester hours. (R.)
Note: Students may not receive credit for both STAT242W and STAT243W.
STAT244 Decision making under uncertainty
A study of the tools and processes for dealing with uncertainty. Topics include the use of prior belief in decision making, updating belief based on evidence, and some of the different methodologies for analyzing data to achieve these aims. Prerequisite: None. Offered in the Spring semester. Three hours per week. Four semester hours.
STAT342. Applied Regression Models
A study of regression models. This course will begin by reviewing simple linear regression and progress to more general modeling approaches including multiple regression models and generalized linear models. Models, inferences, diagnostics, and remedial measures for dealing with invalid assumptions will be examined. Prerequisites: STAT242W or 243W or ECON300Q or permission of instructor. Offered in the spring semester of even years. Three hours per week. Four semester hours.
STAT350 Oral Presentation
A statistics 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 (STAT381, 383) and research/independent work (STAT391394, 491, 492).
STAT382. Internship
An academic/work experience related to statistics conducted under the supervision of an internship adviser and an onsite supervisor. Students must document their experience according to the requirements delineated in the College catalogue section on Internships. 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/STAT242 or 243(W), and approval of a faculty internship adviser. Four semester hours. (XLP.)
STAT384. Internship in Biostatistics
An academic/work experience related to statistics conducted under the supervision of an internship adviser and an onsite supervisor. Students must document their experience according to the requirements delineated in the College catalogue section on Internships. 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/STAT242 or 243(W), and approval of a faculty internship adviser. Four semester hours. (XLP.)
STAT392. Research/Independent Work
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.
STAT394. Independent Study
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. (XLP.)
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.
STAT441W. Applied Research Seminar in Biostatistics
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/STAT242 or MATH/STAT243W and written permission of a department faculty member required. Four semester hours. (R.)
STAT443W. Statistical Modeling
This course will delve into the mathematical and theoretical underpinnings of linear regression, Analysis of Variance (ANOVA), nonparametric statistics and Bayesian methods for statistical inference. This course will satisfy the college requirement for a capstone experience in the major. Prerequisite: MATH 235 and MATH 442 or permission of the instructor. Offered in the fall semester. Three hours per week. Four semester hours.
STAT444. Applied Consulting
The aim of this course is for students to gain practical experience in the application of statistical methods to real data, as well as how to engage with collaborators in a professional setting. Prerequisite: STAT 342 or permission of the instructor. Three hours per week. Four semester hours. This course may count towards the XLP.
STAT451. Topics in Advanced Statistics Faculty
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. (R.)