Mathematics, Computer Science and Statistics

Professor Scoville (Chair); Associate Professors Kozhushkina, Mongan, Sadowski; Assistant Professors Grossbauer, Montesinos-Yufa, New, Takyi, Tralie; Instructors Adam, Henry, Krise.

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.

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 non-technical 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:

• MATH-112, 211, 235, 236W, 311, and 335
• CS-350 or MATH-350
• At least four other mathematics courses at the 300- or 400-level, one of which must be a 400-level capstone course. MATH-400 does not count as an elective towards the math major.
• CS-173

Internships (MATH-381, 382), one-credit and two-credit research/independent work courses (MATH-391-392), and MATH-400 do not fulfill any requirements for the major. Mathematics majors fulfill the requirement for an oral presentation in the major by taking MATH-350 or CS-350 and the capstone requirement by taking one of the following: MATH-413, 421, 434, 442 or 492W.

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. Requirements for Students Pursuing Teaching Certification in Mathematics 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 STAT-141Q, 242. If the student can take 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. There is both a departmental and college minimum GPA requirement for student teaching.

Pre-Engineering

Students interested in pursuing pre-engineering 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 student-initiated 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 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-310, 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: CS-174, CS-375, STAT-141Q, MATH-310, 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. PHYS-111 and 112, are recommended. 

Requirements for Minors in Mathematics

A minor in mathematics consists of MATH-112, 211, 235; and two additional courses in mathematics chosen from MATH-236W, 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:

• MATH-112
• STAT-141
• STAT-142
• MATH-211
• MATH-235
• STAT-240 or DATA/STAT-150
• STAT-242W or STAT-243W
• MATH-341
• STAT-342
• STAT- 350, CS-350 or MATH-350
• MATH-442
• STAT-443W
• At least two of the following: MATH-311, MATH/STAT-343, STAT- 244, STAT-444, CS-377, CS-477, ECON-300Q

Internships (STAT-381, 382) and one-credit and two-credit research/independent work courses (STAT-391-392) do not fulfill any requirements for the major. Statistics majors can fulfill the requirement for an oral presentation in the major by taking STAT-350, CS-350, or MATH-350 and the capstone requirement by taking STAT-443W.
While STAT-394 always fulfills the XLP requirement for the college, STAT-394 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:

• STAT-141Q, 142, 240
• STAT-242W or 243W
• Two additional courses selected from among MATH-341, 442; DATA/STAT-150, STAT-244, 342, 343, 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; PSYC-100; HS-100; or ENVS-100
• STAT-141Q, 142, 240, 243W
• one course selected from among STAT-342, 384, or 441. 

Computational Biology

Computational biology is an interdisciplinary minor consisting of courses in biology, computer science, and statistics. It is only available for students majoring in either biology, BCMB, computer science, or statistics.

Requirements for Minors in Computational Biology (Biology or BCMB Major, 25 Credits)

• CS-173, 174, 274
• STAT-141, 142, 243
• DATA/STAT-150 or STAT-240

Requirements for Minors in Computational Biology (Computer Science Major, 25 Credits)

• STAT-141, 142, 243
• DATA/STAT-150 or STAT-240
• BIO-101, 101L, 102, 102L
• BIO-201W or 225

Requirements for Minors in Computational Biology (Statistics Major, 24 Credits)

• CS-173, 174, 274
• BIO-101, 102,
• BIO-201W or 225

Computer Science

CS-010. Computational Problem Solving

This workshop course offers a structured environment for helping students become better and more efficient computational problem-solvers. Focus is on the computing techniques and tools for advanced productivity in the rapid development of software, and on providing an equitable and inclusive computing environment for collaborative problem solving. May be repeated four times for credit toward graduation. Graded S/U. One hour per week One semester hour.

CS-170Q. 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: CS-170Q 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.
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CS-173. 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 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. (Q, R.)

CS-174. Object-Oriented Programming

A continuation of CS-173. 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 CS-173. Offered every semester. Three hours of lecture and one hour of lab per week. Four semester hours. (R.)

CS/PHIL-243. Technology and Ethics

Data privacy, digital surveillance, data mining, self-driving cars, artificial intelligence, algorithms used by government and law enforcement, doxxing - technology raises many new and old ethical questions. In this core capstone course we use a variety of ways of asking to address these ethical questions: empirical, philosophical, political, creative, and other ways of asking. Three hours per week. Four semester hours. (CCAP, H, O.)

CS-271. 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: MATH-111 or equivalent and a grade of C– or higher in CS-174, or permission of the instructor. Offered in the fall semester. Three hours per week. Four semester hours.

Note: Students who completed CS-371W can not enroll in CS-271.

CS-272. Seminar in Computer Science I

A detailed study of a selected topic in computer science, such as computational geometry, compilers, data mining, robotics or distributed technology. May be repeated for credit. Three hours per week. Four semester hours.

CS-274. Computer Architecture and Organization

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-350. 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 (CS-381, 383) and research/independent work (CS-391-394, 491, 492).

CS-352. Computer Science Pedagogy

This course is a collaborative service-learning effort among students with an interest in computing and in education. The course is intended to prepare pre-service teachers for certification in K-12 Computer Science in Pennsylvania, and to provide students with a research-based background in science communication and pedagogy. We explore unique aspects of educational design in a computing environment, as well as current challenges, trends, and opportunities in computing education. Particular emphasis will center upon equitable computing pedagogy and practice, and creating a classroom environment that is inclusive of diverse learning needs, culturally relevant, and learner-centric. Students will design educational activities according to pedagogical best practices, and work with K-12 teachers at local schools to deliver and assess those educational materials. Students will collectively create a portfolio of open-source curricular materials for teaching computing in the K-12 classroom for subsequent adoption and revision. Offered in the fall of odd years. Three hours per week.Four semester hours. (LINQ with EDUC-350W.)

CS-372. Digital Musical Audio Processing

This hands-on course will take a broad overview of how to represent, analyze, and morph/transform digital musical audio with a computer. Topics include time-domain audio processing, digital instrument synthesis (including FM synthesis), frequency domain audio processing and Fourier analysis, vocoders and cross-synthesis, audio novelty for tempo estimation / beat-tracking, pitch and timbre features, content-based music audio retrieval (e.g., version identification and the “Shazam algorithm”), automatic source separation, and audio mosaicing. Prerequisite: MATH-111 and CS-174 (or CS-173 with permission of the instructor). Offered in spring of odd years. Three hours per week. Four semester hours.

CS-373. 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 Cook-Levin theorem. Emphasis on writing proofs of theorems. Prerequisites: MATH-236W, a grade of C– or higher in CS-174. Offered in the fall of odd years. Three hours per week. Four semester hours.

CS-374. 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 CS-174. Offered in the fall of even years. Three hours per week. Four semester hours.

CS-375. Software Engineering

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: A grade of C– or higher in CS-271. Offered in the spring semester. Three hours per week. Four semester hours. (Q.)

Note: Students who completed CS-275 cannot enroll in CS-375.

CS-376. 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 co-requisite: CS-274. Offered in the spring of even years. Three hours per week. Four semester hours.

CS-377. Database Design

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-271. Offered in the fall of odd years. Three hours per week. Four semester hours.

CS-381. Internship

An academic/work experience under the supervision of an internship adviser and an on-site 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.)

CS-382. Internship

An academic/work experience under the supervision of an internship adviser and an on-site 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.

CS-391. 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.

CS-392. 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.

CS-394. Independent Study

Independent investigation of an area of computer science not covered in regular courses. Students will present a proposal to a faculty member that outlines the research questions, background study, and final products of the project. It is recommended that students first pursue an exploratory independent study project with that faculty member in CS-391 or 392 as they develop this proposal. 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 XLP requirement for the college, but may satisfy an elective requirement for the major only with prior permission of the department chair

CS-472. Advanced Seminar in Computer Science

A detailed study of an advanced topic in computer science that builds upon foundational study in the major. The course will cover topics similar to those listed in CS-272. May be repeated for credit. Three hours per week. Four semester hours.

CS- 474. Human-Computer Interaction

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-375. Offered in the spring semester of even years. Three hours per week. Four semester hours.

CS-475. Computer Networks

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

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 object-first 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 real-time software implementations of shading via the OpenGL Shading Language (GLSL). Prerequisites: CS-271 or 274. Offered fall of even years. Three hours per week. Four semester hours. (LINQ if concurrently enrolled in DIGS-250).

CS-477. 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: MATH-111; CS-271 or 274. Offered in fall of odd years. Three hours per week. Four semester hours. (O.)

CS-491. 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.

CS-492W. 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: 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. (XLP.)

Mathematics

MATH-010. Problem-Solving

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-110. 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 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. (R.)

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

MATH-111. 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 MATH-110. Offered both semesters. Four hours per week. Four semester hours. (Q, R.)

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

MATH-112. Calculus II

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. (Q, R.)

MATH-211. Multivariable Calculus

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. (Q, R.)

MATH-235. 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: MATH-112 or 236W, or permission of the instructor. Offered in the fall semester. Four hours per week. Four semester hours. (R.)

MATH-236W. Discrete Mathematics

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, placement or permission of the instructor. Offered in the spring semester. Three hours per week. Four semester hours. (R.)

MATH/PHIL-260. Logic

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. Three hours per week. Four semester hours. (R.)

MATH-310. 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 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-211 and 235. Offered in the spring semester. Three hours per week. Four semester hours.

MATH-311W. 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: MATH-211 and 236W. Offered in the fall semester. Three hours per week. Four semester hours. 

MATH-312. Analysis II

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. (R.)

MATH-322. Modern Geometry

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. (R.)

MATH-335. 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: MATH-235 and 236W. Offered in the spring semester. Three hours per week. Four semester hours.

MATH-336. 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: MATH-335. Offered in the fall of odd years. Three hours per week. Four semester hours. (R.)

MATH-341. Probability

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. 

MATH/STAT-343. 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. 

MATH-350. 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 (MATH-381, 383, 384, 441) and research/independent work (MATH-391-394, 441, 491, 492W).

MATH-361. 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: MATH-236W. Offered in the fall semester of even years. Three hours per week. Four semester hours.

MATH-381. Internship

An academic/work experience under the supervision of an internship adviser and an on-site 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.)

MATH-382. Internship

An academic/work experience under the supervision of an internship adviser and an on-site 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.

MATH-391. 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.

MATH-392. 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.

MATH-394. 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.

MATH-400. 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 math-phobic. Three hours per week. Four semester hours. (CCAP.)

Note: MATH-400 does not count as an elective towards the math major or minor. The course does not count towards the (R) college core requirement.

MATH-411. Complex Numbers

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. Prerequisites: MATH-236W and 211. Offered in the spring semester of even years. Three hours per week. Four semester hours. 

MATH-413. 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: MATH-211. Offered in the fall semester of even years. Three hours per week. Four semester hours. (R.)

MATH-421. 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. 

MATH-434. Number Theory

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.

MATH-442. 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: MATH-341. Offered in the spring semester. Three hours per week. Four semester hours. 

MATH-451. 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.)

MATH-452. 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.)

MATH-491. 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.

MATH-492W. 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: 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. (XLP.)

Statistics

STAT-140Q. 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.

STAT-141Q. 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.

STAT-142. R Lab

Introduction to the use of computer program R to implement basic statistical techniques. Topics include: graphics, correlation, t-tests, significance testing for proportions and regression. Students pursuing a statistics major or minor should take this concurrently with STAT-141Q. Offered every semester. One hour per week. One semester hour.

STAT/DATA-150. R for Data Science

A hands-on study of the statistical programming language R for liberal arts students. This course prepares students to collect, manipulate, analyze, and visualize real-world 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, data-table, and the tidyverse suite. Examples will be drawn from various disciplines centered on students’ interests. Offered in Spring. Prerequisites: STAT-142 and either CIE-100 or CIE-150 or CIE-200, or permission from the instructor. Four hours per week. Four semester hours.

STAT-240. 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/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-242W Statistics II

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: STAT-142 and STAT-141Q or MATH-442. Offered in the spring semester. Four hours per week.Four semester hours.

Students may not receive credit for both STAT-242W and STAT-243W

STAT-243W Biostatistics

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: STAT-141Q and STAT-142. Offered in the fall semester. Four hours per week. Four semester hours. (R.)

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

STAT-244 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.

STAT-342. 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: STAT-242W or 243W or ECON-300Q or permission of instructor. Offered in the spring semester of even years. Three hours per week. Four semester hours. 

STAT-350 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 (STAT-381, 383) and research/independent work (STAT-391-394, 491, 492).

STAT-382. Internship

An academic/work experience related to statistics conducted under the supervision of an internship adviser and an on-site 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/STAT-242 or 243(W), and approval of a faculty internship adviser. Four semester hours. (XLP.)

STAT-384. Internship in Biostatistics

An academic/work experience related to statistics conducted under the supervision of an internship adviser and an on-site 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/STAT-242 or 243(W), and approval of a faculty internship adviser. Four semester hours. (XLP.)

STAT-392. 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.

STAT-394. 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.

STAT-441W. 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/STAT-242 or MATH/STAT-243W and written permission of a department faculty member required. Four semester hours. (R.)

STAT-443W. Statistical Modeling

This course will delve into the mathematical and theoretical underpinnings of linear regression, Analysis of Variance (ANOVA), non-parametric 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.

STAT-444. 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.(XLP, if approved).

STAT-451. 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.)