Courses

Consideration of diverse subjects in mathematics. Content varies from semester to semester with specific subject matter for each course announced just prior to enrollment. Designed for non-majors who wish to study mathematics other than calculus. This is the preferred course for students interested in taking just one mathematics course at the College.

A version of Mathematics 135 that is designed for students who require more class time to make the transition to college-level mathematics. See the description of Introductory Courses before choosing this course. See the description of Mathematics 135 for the course content. This course meets five hours per week.

This is the standard version of Calculus at the College. Considers the calculus of real-valued functions of one variable for students who are planning further course work in mathematics, a major in the social or physical sciences, or the premedical program. Emphasis is placed on a conceptual understanding of calculus, presenting material from symbolic, numerical, and graphical points of view. The concepts of limit, continuity, and derivative are developed and applied to algebraic, logarithmic, exponential and trigonometric functions.Applications of the derivative are explored. This course meets three hours per week.

Considers the calculus of real-valued functions of one variable for students who are planning further course work in mathematics, a major in the social or physical sciences, or the premedical program. Emphasis is placed on a conceptual understanding of the calculus, presenting material from symbolic, numerical, and graphical points of view. Course content include the theory, evaluation, and applications of integration, sequences and series including Taylor polynomials and series, and an introduction to ordinary differential equations. This course is the prerequisite for Mathematics 241. This course meets four hours per week.

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers).

A study of the calculus of functions of several variables. Concerns the theory and applications of differentiation and integration of functions of several variables, vector fields, line integrals, Green's theorem.This course meets four hours per week.

An introduction to the primary algebraic and analytic structures in abstract mathematics. Emphasis is placed on using the language of sets, equivalence relations and functions, and on developing techniques of proof, including elementary logic and mathematical induction, basic group theory, and limits.

Designed to acquaint students with the basic techniques of linear algebra. Topics include matrices, vector spaces, subspaces, linear transformations, bilinear forms, determinants, eigenvalue theory, and the finite dimensional spectral theorem. Applications and additional topics are included as time permits.

Centers on some area of geometry other than differential geometry. Possible topics include Euclidean and non-Euclidean geometry, projective geometry, the geometry of transformation groups, and the elementary geometry of algebraic curves.

A first course in the differential geometry of curves and surfaces for students who have completed Mathematics 241 and a semester course in linear algebra. Topics include the Frenet-Serret formulas, smooth surfaces in 3-space, fundamental forms, differentiable manifolds, vector fields, connections and a brief introduction to Riemannian geometry.

Introduction to the role of mathematics as a modeling tool, including the construction, interpretation and application of mathematical models. Applications chosen to illustrate various modeling paradigms such as deterministic, probabilistic, discrete and continuous modeling and may include population dynamics, biomedical applications, stock market analysis, and network and traffic flows.

Linear differential equations are studied; basic existence theorems are proved. Separation of variables, Laplace transforms, first- and second-order equation and linear systems, and topics in nonlinear systems are considered. Breadth area: Applied Mathematics/Statistics.

The fundamentals of complex analysis. Topics include the complex number system, analytic functions, the Cauchy-Riemann equations, Cauchy's integral theorem, Cauchy's integral formula, Taylor series, Laurent series, the calculus of residues and conformal mapping.

An in-depth study of the structure of groups, rings and fields. Depending on the instructor, applications to Galois theory, number theory, geometry, topology, physics, etc., are presented.

A continuation of Mathematics 351 exploring advanced topics and applications in modern algebra.

Elementary number theory is concerned with properties of numbers (integers, primes, etc.) as well as patterns and relationships among certain sets of numbers. Topics will include divisibility, congruences, special types of primes, the distribution of primes throughout the integers, number-theoretic functions, quadratic residues, and continued fractions. Further study may include the RSA code, a superior encryption algorithm based on elementary number theory, and a discussion of one of the most famous problems in mathematics - Fermat's Last Theorem - conjectured in 1630 yet unsolved until the 1990s.

An introduction to the subject that discusses a representative sampling of combinatorial problems and general techniques for solving them, including a selection of counting techniques, techniques for existence questions, and a variety of examples. Examples may include partitions, graphs and trees, tournaments, graph coloring and chromatic polynomials, magic squares, Latin rectangles and squares, and combinatorial block designs.

Topological ideas are introduced through a treatment of metric space topology. After the study of open, closed, compact and connected spaces with emphasis on their behavior under continuous mappings, selected topics from functional analysis are considered. These include lim sup and lim inf, relation of uniform convergence to differentiation and integration, and the Stone-Weierstrass approximation theorem.

A continuation of Mathematics 361 exploring advanced topics, including an introduction to Lebesgue-Stieltjes integration, Hilbert space and other material from linear space theory.

Considers various aspects of topology of surfaces and solids, including orientability, the Euler number, and the fundamental group. One of the goals of the course is the topological classification of surfaces.

The numerical solution of problems using computers. Considerable time is devoted to selecting the appropriate algorithm for a given problem and analyzing the resulting numerical errors. Includes such topics as error analysis of computer arithmetic, approximation of functions, solution of equations, numerical integration, numerical solution of ordinary differential equations.

Provides an understanding of a wide spectrum of phenomena through the use of mathematical ideas, abstractions, and techniques. Topics included are partial differential equations, including the heat and wave equations, Fourier analysis, eigenvalue problems, Green's functions.

An introduction to the theory of discrete dynamical systems. Topics include iteration of functions, graphical analysis, periodic points, stable sets, chaos, symbolic dynamics, the dynamics of functions of a complex variable and the Mandelbrot set. The major theorems will be studied along with their proofs and the computer will be used as a research tool to do experiments which motivate and illustrate the theory.

Provides an opportunity for individual and group investigation of topics not covered in ordinary course work. Active participation on the part of the students is normally required. Subject matter varies to suit individual students and is often related to the research activity of the professor. Examples of areas of study: Lie groups, functional analysis, complex analysis, probability theory, commutative algebra, applied mathematics, the classical groups, mathematical logic, automata and formal languages, topics in discrete modeling, and qualitative theory of differential equations.

An independent reading project for upper division students. Normally this is on a topic that is not covered by the regular course offerings. Permission of the instructor and the department chair is required for this course.

A project course for upper division students under the direction of a faculty member. Normally the project will provide an introduction to research on a topic that is not covered by the regular course offerings. Course requirements are to be arranged in consultation with the instructor. Permission of the instructor and the department chair is required for this course.

A large project extending over the course of the fourth year. It can consist of original research or be of an expository nature and is written under the guidance of one or more members of the department. Normally, a student will earn one unit in the spring semester of the fourth year for successful completion of an honors thesis, unless the thesis work is done as part of the student's participation in a departmental seminar. In that case, no extra credit is given above the credit for the seminar itself. For a particularly extensive project, and with the permission of the department chair, a student may earn one unit in each semester of the fourth year for completion of the thesis.

A large project extending over the course of the fourth year. It can consist of original research or be of an expository nature and is written under the guidance of one or more members of the department. Normally, a student will earn one unit in the spring semester of the fourth year for successful completion of an honors thesis, unless the thesis work is done as part of the student's participation in a departmental seminar. In that case, no extra credit is given above the credit for the seminar itself. For a particularly extensive project, and with the permission of the department chair, a student may earn one unit in each semester of the fourth year for completion of the thesis.

A survey of the science and art of computing intended for students not majoring in mathematics or science. Half of the course is an introduction to computer programming. Emphasis is placed upon language independent topics such as structured programming, good programming style, the use of subprograms, and algorithm construction in general. The other half of the course explores how computers are built, how they operate, and what their fundamental limitations are.

A broad introduction to fundamental concepts in computer science, with emphasis on designing and writing correct and elegant computer programs. Concepts are illustrated through examples drawn from a variety of application areas and may include graphics, digital media, scientific computing, or games. Weekly lab meetings provide supervised practice. This course is appropriate for any student interested in creating or understanding software, and students with little or no prior programming experience are welcome. Students in this course develop both real-world programming skills and gain a foundation for applications in mathematics, the sciences, economics, accounting, or any other discipline in which computing plays an important role. This course also prepares students for further study in Computer Science 132, Data Structures, and it is required for both the major and the minor.

An introduction to techniques for storing and manipulating complex data. Students gain experience with sophisticated programs by studying frequently used data structures, including stacks, lists, trees, graphs, and hash tables, and by discussing algorithms for searching, sorting, graph traversal, and hashing. Weekly lab meetings provide supervised practice designing, implementing and using these data structures. As time allows, students also begin an introduction to analysis of algorithms by examining the space and time efficiency of data structures and related algorithms. This course is required for both the major and the minor.

An introduction to the discrete mathematical structures that form the basis of computer science. Topics include proof techniques, relations and functions, set theory, Boolean algebra and propositional logic, predicate calculus, graphs, trees, induction and recursion, counting techniques and discrete probability. It is recommended this class be taken concurrently with Computer Science 132.

This course is intended for students interested in improving their programming skills through practice with modern Java concepts and Object Oriented Programming. Topics may include exception handling, standard library collections and templates, inheritance, polymorphism, overloading, interfaces, and iterators, for-each loops. Students will complete guided and independent projects, including group projects.

This course is about modern tools, platforms, and practices for software development and operations, commonly known as DevOps. The main focus will be towards Continuous Integration / Continuous Delivery. Students will also gain experience working with tools used commonly for careers in software engineering, development, and operations, such as Amazon Web Services EC2, Agile development practices, source code management using git, virtualization platforms like Docker, and monitoring using DataDog or JMeter/Gatling.

Covers fundamental topics related to the design and operation of a modern computing system. Relationships are drawn between circuits and system software. Topics include hardware and software organization, virtual machines, physical fundamentals of transistors, digital logic design, memory system organization, architecture and management, CPU design, multiprocessors, data representation, machine language, microprogramming, assembly language, assemblers and linkers, CISC versus RISC, interrupts and asynchronous event handling, networking, and the past and present of computer system design, architecture, and organization.

Provides an introduction to the design and analysis of fundamental algorithms and their complexity. Presents several algorithm design strategies that build on the data structures and programming techniques introduced in Computer Science 132. The general techniques covered include: Divide-and-conquer algorithms, dynamic programming, greediness and probabilistic algorithms. Topics include: sorting, searching, graph algorithms, O-notation, and introduction to the classes P and NP, and NP-completeness.

In this project-based course, students work in teams to complete a semester-long project following software engineering best practices. The resulting minimal viable product may be a web application or other interactive software, and will involve planning, database integration and testing, and presentations. Students consider the life cycle of large software projects, beginning with the elicitation and definition of users' requirements and continuing through software design, documentation, coding, testing and maintenance. Topics include: modularity, coupling, cohesion, transformational and transactional structures and testing strategies. Working in teams, students gain practical experience developing software to solve concrete problems.

Data Mining refers to the process of extracting useful models of data. Sometimes, a model can be a summary of the data, or it can be the set of most extreme features of the data. Computer scientists often approach data mining in one of two ways, as an algorithmic problem or by using data along with a machine learning engine. This course provides an introduction to Data Mining and will examine data techniques for the discovery, interpretation and visualization of patterns in large collections of data. Topics covered in this course include data mining methods such as classification, rule-based learning, decision trees, association rules, and data visualization. The work discussed originates in the fields of artificial intelligence, machine learning, statistical data analysis, data visualization, databases, and information retrieval.

Principles for designing and implementing programming languages are presented as well as styles and features that encourage and discourage the writing of good software. Topics include language syntax and semantics, comparison of language features and their implementation, methods of processing a program, establishing the run-time environment of the program and the major programming language paradigms (the imperative/procedural, functional/applicative, declarative/logic and object-oriented paradigms).

This course presents the fundamental concepts and principles of computer security. Topics include cryptographic tools, user authentication, access control, malicious software, denial-of-service attacks, intrusion detection, and intrusion prevention systems. Software security and operating system security are studied in detail. Additional areas of study may include security management, risk assessment, human resources security and the many legal, social, and ethical aspects of computer security.

An introduction to database concepts and database management systems, including the storage, processing, evaluation, display, and security of data. This course focuses on the study of logical and physical database design; fundamental data management and query techniques using SQL, a ubiquitous data query language; and methodologies for database development including relational approaches and object-oriented approaches. Practical skills are emphasized to allow students to create, manage, use, and analyze concrete databases and the corresponding information systems using state-of-the-art industry-standard software products, such as Oracle, Microsoft SQL Server, MySQL or PostgreSQL.

Examines the ethical issues that arise as a result of increasing use of computers, and the responsibilities of those who work with computers, either as computer science professionals or end users. The course stresses the ways in which computers challenge traditional ethical and philosophical concepts, and raise old issues in a new way. Students will be expected to read and understand the ideas in the readings, explain the ideas, analyze issues and see them from diverse perspectives, and formulate and critique arguments. Readings include technical issues in computer science and may focus on a particular area such as software design as well as more traditional topics such as philosophical theories (e.g. ethical relativism, utilitarianism, deontological theories, rights and virtue ethics), privacy, intellectual property rights and proprietary software, security, accountability, liability, the digital divide, hacking, and viruses. There are several course goals: (1) to give a fuller, richer, deeper understanding of the social impact of computers and the ethical issues in human activities affected by computers, (2) to prepare the student for living in a computerized world and perhaps working as a professional in the computing field, and (3) to improve presentation, debating and writing skills.

A survey of topics in computer graphics with an emphasis on fundamental techniques and the theory underlying those techniques. Topics include the fundamentals of two and three dimensional graphics such as clipping, windowing, and coordinate transformations (e.g., positioning of objects and camera), raster graphics techniques such as line drawing and filling algorithms, hidden surface removal, shading, color, curves and surfaces and animation. Students learn how to program graphics displays using a computer graphics package.

This course considers the theoretical foundations of computer science through different computational models. Topics covered in this course include deterministic and non-deterministic finite automata, regular expressions, context-free grammars, pushdown automata, Turing machines, decidability, undecidability, and computational complexity including the P vs. NP problem.

Provides an introduction to the general model of operating systems principles and current implementation techniques. The principles and mechanisms that underlie operating systems services will be covered. Students will learn techniques for managing hardware resources and sharing them among many competing processes and threads. They will study the internal structures needed for process and thread management, synchronization, inter-process communication, memory management (including shared memory), file system management, distributed systems principles, device control, and security.

This course provides an introduction to the field of artificial intelligence. Topics include solving problems using search (e.g., depth-first search, iterative deepening, and A*), constraint satisfaction problems, propositional logic and first-order logic, inference in propositional logic and first-order logic, and machine learning techniques (e.g., decision trees and neural networks).

This course focuses on principles of computer networking. Students will gain an understanding of the low-level protocols that drive the Internet, including protocols for data forwarding, routing, congestion, flow control, reliability, naming, and discovery, along with their application to distributed systems. Topics are introduced from a theoretical perspective, but students will also gain practical experience designing, implementing, and measuring distributed systems, such as web servers, email and messaging systems, video and data distribution, and cloud computing.

An introduction to the algorithms underlying machine and biological visual systems. Examines the processes involved in converting a 2-dimensional image to a 3-D representation of the physical world. Computational models of visual processing will be compared to physiological and psychophysical results from human and other biological visual systems. Topics covered include: edge detection, stereopsis, motion computation, shape from shading, color and object recognition.

The theories, tools and techniques for translator creation are the focus of this course. Topics include: regular expressions, grammars, finite state machines, lexical analysis, parsing, linguistic approaches to problem solving, intermediate code trees, register allocation, code generation, a variety of optimization schemes and techniques as well as Linux-style support for translation such as lex/flex and yacc/bison. An essential and distinguishing feature of the course is the project requirement. Students are required to build a working compiler that is a large software engineering project of significant complexity. This course carries the project course designation.

The course provides a comprehensive study of machine learning techniques, including supervised and unsupervised learning. Topics include supervised learning techniques for classification and regression such as decision trees, k-nearest neighbors, linear models, and neural networks; also includes unsupervised learning techniques such as principal component analysis, clustering etc. The course will also cover the essentials of applied linear algebra and calculus as necessary, and an introduction to Python programming and associated libraries and tools.

An independent reading project for upper division students. Normally this will be on a topic that is not covered by the regular course offerings. Permission of the instructor and the Department Chair is required for this course.

A project course for upper division students under the direction of a faculty member. Normally the project will provide an introduction to research on a topic that is not covered by the regular course offerings. Course requirements are to be arranged in consultation with the instructor. Permission of the instructor and the department chair is required for this course.

This is a large project extending over the course of the fourth year. It can consist of original research or be of an expository nature and is written under the guidance of one or more members of the department. A student will earn at least one unit of credit in the spring semester of the fourth year for successful completion of an honors thesis, unless the thesis work is done as part of the student's participation in a department seminar. In that case, no extra credit is given above the credit for the seminar itself. For a particularly extensive project, and with the permission of the department chair, a student may earn one unit in each semester of the fourth year for the completion of the thesis.

This is a large project extending over the course of the fourth year. It can consist of original research or be of an expository nature and is written under the guidance of one or more members of the department. A student will earn at least one unit of credit in the spring semester of the fourth year for successful completion of an honors thesis, unless the thesis work is done as part of the student's participation in a department seminar. In that case, no extra credit is given above the credit for the seminar itself. For a particularly extensive project, and with the permission of the department chair, a student may earn one unit in each semester of the fourth year for the completion of the thesis.

This course presents the basic concepts of statistics and data analysis in a non-technical way. Topics include graphical methods of summarizing data, descriptive statistics, and methods of statistical inference. STAT 120 is a terminal, introductory course intended for students who are not interested in pursuing mathematics, economics, biology, psychology, sociology, or the health professions.

This course provides an introduction to the field of data science with a focus on computation, data visualization, collaboration, and communication. Students will learn to extract and wrangle data, program basic scripts and functions in an integrated development environment, explore multivariable associations and understand the concepts of confounding and effect modification, create dynamic data visualization, and build interpretable machine learning models.

This course presents statistics intended for students aspiring to the health professions. Topics include sampling strategies and experimental design, numerical and graphical methods of describing data, basic concepts in probability, discrete and continuous probability distributions, sampling distributions, confidence intervals, hypothesis testing and simple linear regression. Statistics is a part of the health professions curriculum, but some majors at the College offer their own statistics courses that are tailored to their respective disciplines. Students majoring in mathematics, economics, biology, psychology and sociology should take the statistics course within their major. Health profession students are advised to wait and take the statistics course in their major, should it offer one. Otherwise, such students should take STAT 220 sometime after their first year at the College.

This course provides an introduction to the statistical methodologies most commonly used in the design of experiments. Topics include experimental design, power and sample size determination, one-sample inference, two-sample inference, multi-sample inference, assumptions testing, linear contrasts, experiment-wise error rate, factorial treatment structure, and interaction. Also covered are equivalent non-parametric tests. Students will work extensively with data sets and the R statistical software package.

While most courses cover statistics from a Frequentist point of view, this course will instead look at statistical inference from a Bayesian perspective. Bayesian statistics combines prior information with the information contained in the observed data to produce a (posterior) probability distribution on a parameter of interest. In the past, computational challenges limited the use of Bayesian techniques, but advances in modern computing along with the introduction of new algorithms that allow for sampling from complex, high-dimensional probability distributions have increased the popularity of these methods. Potential topics will include: an introduction to probability and Bayes rule, prior and posterior distributions, conjugate priors, single and multi-parameter likelihood models (e.g. binomial, Poisson, normal, etc.), Markov Chain Monte Carlo methods, Gibbs sampling techniques, hierarchical modeling, Bayesian analogs to confidence intervals and hypothesis testing, model comparison, model averaging, and Bayesian linear regression.

This course provides a thorough examination of the theory and practice of ordinary least squares (OLS) regression modeling. Model interpretation and a conceptual understanding of confounding, mediation, and effect modification are emphasized. Specific topics include analysis of variance (ANOVA), derivation of parameter estimates, correlation, prediction, dummy variables, contrasts, testing general hypotheses, analysis of covariance (ANCOVA), multicollinearity, regression diagnostics, techniques for handling model misspecification (incorrect functional form, heteroskedasticity), and model-building strategies. Students will work extensively with data sets and the R statistical software package.

This course provides a focused introduction to the theory and practice of categorical data analysis. Model interpretation and conceptual understanding will be emphasized. Specific course topics include the chi-square test for independence, Fisher's exact test, logistic regression, multinomial logistic regression, prediction, dummy variables, contrasts, testing general hypotheses, effect modification and confounding, assessing fit, and model-building strategies. Students will work extensively with data sets and the R statistical software package.

This course introduces the principles and methodologies underlying the design and analysis of observational studies. Observational studies are critical in fields where controlled experiments are impractical or unethical, and offer insights into behaviors and outcomes in real-world settings. Throughout this course, student will explore the challenges and strategies associated with drawing causal inferences from observational data. Topics include the design of observational studies, including cohort, case-control, and cross-sectional studies, as well as techniques for managing common issues such as confounding, selection bias, and measurement error. Students will learn to apply data analysis techniques tailored to observational data, including regression models and propensity score matching. Students will analyze data sets using the R statistical software package.

An introduction to the theory and applications of probability. Includes both continuous and discrete distributions, conditional probability and Bayes' Theorem, random variables and expected values, joint distributions of several random variables, functions of random variables, and the Central Limit Theorem.

A course in the theory and applications of statistics. Topics include maximum likelihood estimation, the sampling distributions of estimators, confidence intervals, hypothesis testing, regression analysis, and an introduction to the analysis of variance.

This course covers statistical methods that would not be possible without the advances made in modern computing over the last 25-30 years. Specifically, these are simulation and Monte Carlo techniques that are appropriate where statistical theory does not yet provide a solution. Each of the statistical methods covered is computationally intensive and therefore requires a computer to arrive at a solution. Topics include techniques for simulating of random variables, Bayesian statistics, Markov chains, the Metropolis-Hastings algorithm, MCMC and Gibbs Sampling, mixture models, and classification schemes.

This course is an introduction to the main principles of supervised and unsupervised machine learning within the context of data analytics. Methods include linear regression, logistic regression, K-nearest neighbors, and discriminant analysis. Resampling methods such as cross-validation and bootstrapping, as well as model selection and regularization techniques are discussed. Non-parametric methods, including classification and regression trees (CART), boosting, bagging, and random forests are presented. Unsupervised learning methods focus on principal components analysis, K-mean, and hierarchical clustering. The R statistical computing package is used extensively.

Provides an opportunity for individual and group investigation of topics not covered in ordinary course work. Active participation on the part of the students is normally required. Subject matter varies to suit individual students and is often related to the research activity of the professor.