43 courses with the subject MATH, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MATH 105Introduction to Statistics1.00
An introduction to the basic concepts of statistics. Topics include experimental design, descriptive statistics, correlation, regression, basic probability, mean tendencies, the central limit theorem, point estimation with errors, hypothesis testing for means, proportions, paired data, and the chi-squared test for independence. Emphasis is on statistical reasoning rather than computation, although computation is done via software. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
An introduction to the basic concepts of differential and integral calculus including limits and continuity; differentiation of algebraic, trigonometric, exponential, and logarithmic functions; applications of the derivative to curve sketching, related rates, and maximum-minimum problems; Riemann sums and the definite integral; and the fundamental theorem of calculus. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
Three years of secondary school mathematics including trigonometry
Corequisite
None
MATH 162Calculus II1.00
A continuation of the study of calculus begun in MATH 161. Topics covered include the calculus of inverse trigonometric functions, techniques of integration, improper integrals, L'Hôpital's rule and indeterminate forms, applications of integration, and Taylor series. Note: MATH 161 may not be taken after credit is earned for MATH 162. calculus course Major/Minor Restrictions: None Class Restriction: None
MATH 161 with a grade of C- or higher or equivalent experience in a secondary school
Corequisite
None
MATH 163Calculus III1.00
The content from MATH 161 and MATH 162 is extended to several variables. Among the topics considered are surfaces in three-dimensional space, partial derivatives, maxima and minima, and multiple integrals. calculus course, or MATH 161 with a grade of B- or better and concurrent enrollment in PHYS 232 Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
MATH 162 with a grade of C- or higher, or equivalent experience in a secondary school
Corequisite
None
MATH 214Linear Algebra1.00
A study of sets of linear equations and their transformation properties over vector spaces. Topics include: systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and diagonalization. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
Provides a comprehensive introduction to the field of statistics and probability and the understanding of scientific programming and simulation. Students learn to clean, summarize, and analyze data in R, focusing on interpretation and extracting information. Coursework aims to expose students to the theory of probability and statistics through computational exercises and topics that provide insight into the essential theories of probability, random variables, expectations, and statistical inference. The required lab portion of the course enables students to implement these ideas in R by exploring real data from several disciplines. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning and The Process of Writing Core Component: None
MATH 161 or equivalent experience in a secondary school calculus course.
Corequisite
MATH 240L
MATH 240LComputational Statistics with R Lab
Required corequisite to MATH 240. Credits: .25 Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: None Liberal Arts Practices: None Core Component: None
Questions about the positive integers 1, 2, 3 . . . have fascinated people for thousands of years. The ancient Greeks noted the existence of right triangles with sides of integral length, corresponding to equations such as 32 + 42 =52 and 52 + 122 = 132. Is there a way of describing all such "Pythagorean Triples?" As another example, the integer 6 is called "perfect" because 6=1+2+3, so that 6 is the sum of its positive factors. There are currently 51 known perfect numbers. Do the perfect numbers follow any pattern? Are there infinitely many of them? Much of this course focuses on such questions as a means for introducing students to the spirit and methods of modern mathematics. Other course content deals with the question of extending the list 0,1,2,3,... so that it will include the number of elements in any finite set, but also the number of elements in any infinite set. The emphasis throughout is on developing the ability to construct logically sound mathematical arguments and communicate these arguments in writing. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
An exploration of computer manipulation and presentation of mathematical ideas. The computer allows mathematics to be explored, manipulated and connected to data. No background in programming is presumed. Students learn how numbers are stored and manipulated on the computer in order to do mathematics (from calculus to linear algebra to exploring patterns in the integers), how mathematical functions can be encoded and presented, and how data relates to functions. Induction and continuity are methods of proof relying on infinity, yet will be explored using the finite number cruncher called a computer. The results provide examples and intuition for further mathematical investigation. The required lab portion of the course allows students to implement these ideas in practice. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics
Required corequisite to MATH 260. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
Opportunity for individual study in areas not covered by formal course offerings, under the guidance of a member of the faculty. Credits: variable Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
Systems biology is an emerging interdisciplinary field that employs quantitative methodologies to gain a system-level understanding of the complex interactions of biological processes. Students focus on the applications of mathematical techniques such as differential equations, machine learning, network science, and modeling (e.g., Boolean and stochastic modeling) to the study of gene regulation, signal transduction pathways, small- and large-scale biological networks, and human diseases. Students also learn how to analyze biological questions using computer software. Crosslisted: BIOL 302 When Offered: Fall semester only, in alternate years Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
Differential Equations relate unknown functions to their derivatives. Finding the solution involves identifying functions that satisfy that equation. This course focuses on techniques for solving ordinary differential equations as well as some basic general theory of ordinary differential equations. Topics include: first order equations with associated initial conditions, linear higher order equations with constant coefficients, systems of linear and nonlinear differential equations, and solutions written as power series and/or using transforms. Applications are presented. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
Develops methods to solve combinatorial (finite) problems arising in mathematics, computer science, and other areas from the natural and social sciences. Enumeration and graph theory are the main subjects. Topics include recurrence relations, generating functions, inclusion-exclusion, modeling with graphs, trees and searching, graph coloring, and network algorithms. The emphasis is on problem solving rather than theory. When Offered: Fall semester only Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
By introducing the imaginary number i = √-1 the analysis of functions over the complex plane becomes, at times, distinctly different than over the real plane. Topics include complex numbers and functions, the theory of differentiation and integration of complex functions, sequences and series of complex functions, and conformal mapping. Special attention is given to Cauchy's integral theorem. When Offered: Fall semester only, in alternate years equivalent of MATH 162 in other courses, shall consult with the instructor Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
MATH 162 and MATH 163. Students who have not taken MATH 162, but have learned the
Corequisite
None
MATH 315Mathematical Biology1.00
Mathematical biology is a fast growing and interdisciplinary area in which mathematics is utilized as a tool for studying various biological phenomena such as population growth, infectious diseases, the spread of invasive species, cell movement, dynamics of a neuron, etc. This course provides an introduction to the basics of discrete and continuous models and mathematical concepts for students to learn how to derive, interpret, solve, simulate, and understand models of biological systems. When Offered: Fall semester only, in alternate years Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics
An introduction to the basic concepts of discrete and continuous probability: axioms and properties of probability, standard counting techniques, conditional probability, important random variables and their discrete and continuous distributions, expectation, variance, moment generating functions, transformations, and joint distribution functions. Additional topics may include: Markov chains and Monte Carlo methods. When Offered: Fall semester only Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
MATH 354Data Analysis I - Generalized Linear Models1.00
An applied course on linear models, an umbrella term that covers a wide range of statistical models widely used today across disciplines in academic research and industry. Building on simple linear regression, students explore multiple linear regression with both quantitative and qualitative explanatory variables. Students investigate model building, assessment of assumptions with model diagnostics and residual analyses, and the interpretation of results via statistical inference, untangling interaction terms, and post hoc analyses. This discussion is then extended to analysis of variance (ANOVA), generalized linear models, and mixed effects models. While applied, coursework aims to combine theory and application to emphasize the need for understanding each method's theoretical foundation. Through iterative practice with scientific writing, students also learn to effectively communicate quantitative information. The statistical software R is used for all analyses. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning and The Process of Writing Core Component: None
An investigation of the properties and structure of graphs. Graph theory uses mathematical constructs called graphs to approach a diverse set of problems that have nontrivial applications in computer science, operations research and other disciplines. It is one of the very few mathematical areas where one is always close to interesting unsolved problems. Topics include graphs and subgraphs, trees, connectivity, Eulerian and Hamilton cycles, matchings, colorings, planar graphs, directed graphs, network flows, counting arguments, and graph algorithms.
An introduction to both point-set topology and basic algebraic topology. Topics include metric spaces, topological spaces, compactness, connectedness, the classification of surfaces, mod-2 homology, and the Jordan curve theorem. Additional topics that demonstrate connections with analysis, dynamics, and algebra are determined by the instructor based on student interest. When Offered: Spring semester only, in alternate years Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
Abstract algebraic structures, rather than results specific to the usual number systems, are developed. Basic algebraic structures presented include groups, rings, integral domains, and fields. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
An introductory treatment of methods used for numerical approximation. Topics include: roots of equations, simultaneous linear equations, quadrature, and other fundamental processes using high speed computing devices.
Results from calculus, including limits, continuity, the derivative, and the Riemann integral, are given a rigorous treatment. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
MATH 162 and MATH 163 and (MATH 250 or MATH 260) with a grade of C or better
Corequisite
None
MATH 391Independent Study
Opportunity for individual study in areas not covered by formal course offerings, under the guidance of a member of the faculty. Credits: variable Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
Explores mathematics as it is applied to the physical sciences. Mathematical topics may include boundary value problems, partial differential equations, special functions, Fourier series and transforms, Green's functions, and approximate solution methods. When Offered: Fall semester only, based on demand Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
Matroids take varying notions of "independence" within different areas of mathematics -- including linear algebra, graph theory, geometry, and abstract algebra -- and form a way to unite them. This single idea, first studied in 1935, turned out to form an immensely powerful framework that is among the most active areas of research within discrete mathematics. For example, it turns out that greedy algorithms are possible exactly when there is a matroid lurking in the background. Students are introduced to the fundamentals of matroid theory, with an emphasis on geometry. Topics include graphic matroids, representable matroids, affine and projective finite geometries, hyperplane arrangements, operations on matroids, and the Tutte polynomial. When Offered: Fall semester only, in alternate years, based on demand Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
Building on the material learned in MATH 316, students examine the theoretical underpinning of statistical results. Topics include theoretical explorations of limit theorems, estimation, sampling distributions, confidence intervals, and tests of hypotheses. More specifically, students explore sufficiency, maximum likelihood techniques, minimum variance principles, uniformly most powerful tests, pivotal quantities, test inversions, and asymptotic evaluation with the choice of additional topics determined by the instructor (e.g., Bayesian and nonparametric estimation). While the primary focus is on the theory of statistics, students will learn to conduct and evaluate these approaches via simulation using the statistical software R. Students may find MATH 416 a useful companion to the application-focused MATH 354. When Offered: Spring semester only, in alternate years, based on demand
A systematic study of continuous random processes through the lens of Brownian motion and the associated calculus, achieved via a balance of theory and numerics. Topics include: Gaussian processes, Brownian motion, conditional expectations, martingales, Itô's formula, Itô processes, and stochastic differential equations. Applications to finance, physics, and computer science are illustrated. When Offered: Fall semester only, in alternate years, based on demand Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
MATH 214 and (MATH 240 or MATH 250 or MATH 260) and (MATH 316 or MATH 377)
Corequisite
None
MATH 448Nonlinear Dynamics & Chaos1.00
An introduction to the techniques and concepts used to analyze real-time dynamic models that involve nonlinear terms. Applications are highly emphasized and include interdisciplinary topics such as biological population dynamics, mechanical systems, oscillating chemical reactions, electrical circuits and synchronization. This course is team-taught by members of the physics and mathematics departments. Crosslisted: PHYS 448 When Offered: Spring semester only, in alternate years Major/Minor Restrictions: None Class Restriction: None Recommended: Students should enroll through the department for which they intend to use the credit. Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: Quantitative and Algorithmic Reasoning Core Component: None
Continues the study of number theory begun in MATH 250 and includes the Quadratic Reciprocity Law of Gauss, the Cubic Reciprocity Law of Eisenstein and Jacobi, and other topics from algebraic number theory.
An applied regression course that involves modeling and interpreting data with statistical learning methods in regression and classification. Topics include K Nearest Neighbors, Logistic Regression, Discriminant Analysis, Ridge Regression, LASSO, Regression Splines, Generalized Additive Models, Tree-Based Models, and Support Vector Machines, with the choice of additional topics determined by the instructor (e.g., Bootstrapping, Principal Components Analysis, Latent Profile Analysis, Clustering, structural equation models). While applied, it aims to combine theory and application to emphasize the need for understanding each method's theoretical foundation. This conversation is had through illustrating a variety of inferences, residual analyses and fully exploring the implications of our assumptions. When Offered: Spring semester only, in alternate years, based on demand Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: The Process of Writing Core Component: None
Introduces the notions of Hilbert and Banach spaces. A thorough understanding of these types of spaces is crucial in several areas of mathematics and applied mathematics. For example, quantum theory can be formulated in terms of operators on infinite dimensional Hilbert spaces. Students are also introduced to the notion of basis and frames in finite and infinite dimensions. In finite dimensions frames are spanning sets for a vector space. When Offered: When Offered: Fall semester only, in alternate years, based on demand Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
This capstone seminar presents senior Applied Mathematics majors with a research experience in applied mathematics. Each student will work closely with the instructor on a research problem that will require the integration of previously developed applied mathematics skills. Students will apply their learning from previous math courses toward a specified research problem and will delve deeply into material related to the specific problem. Each student will complete a written piece of mathematics addressing their research problem and will present their work as a final thesis. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: The Process of Writing Core Component: None
This capstone seminar presents senior Mathematics majors with a research experience in mathematics. Each student will work closely with the instructor on a research problem that will require the integration of previously developed mathematics skills. Students will apply their learning from previous math courses toward a specified research problem and will delve deeply into material related to the specific problem. Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: The Process of Writing Core Component: None
Continues the study of abstract algebraic structures, providing a careful and intensive study of topics such as group theory, ring theory, field theory, and Galois theory. When Offered: Spring semester only, in alternate years Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
Topics for this course are selected from among the following: metric spaces, sequences and series of functions, the Lebesgue integral. When Offered: Spring semester only, in alternate years Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
Set theory serves as a foundation for all of mathematics, in the sense that all of the objects and constructions of mathematics can be expressed in terms of sets. It was discovered over 100 years ago, however, that intuitive set theory is riddled with contradictions. This course introduces students to the axioms of Zermelo-Fraenkel set theory, which restrict the ways in which sets can be formed, in the hope of avoiding the contradictions. Topics include the Zermelo-Fraenkel axioms and some of their consequences; well-orderings and various statements equivalent to the axiom of choice; and ordinal and cardinal numbers. When Offered: Fall semester only, in alternate years, based on demand Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None Formerly: MATH 389
Opportunity for individual study in areas not covered by formal course offerings, under the guidance of a member of the faculty. Credits: variable Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
The topics covered include the following: propositional and predicate calculus, completeness and compactness theorems, the foundations of nonstandard analysis, first-order model theory, recursive functions, a full proof of Godel's Incompleteness Theorem, and undecidability. When Offered: Fall semester only, in alternate years, based on demand Major/Minor Restrictions: None Class Restriction: None Area of Inquiry: Natural Sciences & Mathematics Liberal Arts Practices: None Core Component: None
