Mathematics Classes

This course focuses on calculus useful for both theoretical and applied work in the mathematical, natural, and social sciences. Topics include: partial derivatives, gradients, contour plots, constrained and unconstrained optimization, Taylor polynomials, interpretations of integrals via finite sums, the fundamental theorem of calculus, double integrals over a rectangle,and differential equations. Attention is given to both symbolic and numerical computing. Prerequisite(s): MATH 135 or a year of high school calculus at the level of AP calculus with an AB score of 4 or higher.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Linear algebra is one of the pillars of mathematics, both pure and applied. Linear relations can be used to model phenomena from numerous disciplines in the mathematical sciences, physical sciences, social sciences, engineering, and computer science. This introduction to linear algebra blends mathematical computation, theory, abstraction, and application. It starts with systems of linear equations and grows into the study of matrices, vector spaces, linear independence, dimension, linear transformations, orthogonality and projections, eigenvectors, and their applications. The resulting linear algebraic framework is a flexible and powerful way to approach multidimensional problems. Prerequisite(s): MATH 279 or MATH 137, or with permission of instructor, MATH 135 .

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Linear algebra is one of the pillars of mathematics, both pure and applied. Linear relations can be used to model phenomena from numerous disciplines in the mathematical sciences, physical sciences, social sciences, engineering, and computer science. This introduction to linear algebra blends mathematical computation, theory, abstraction, and application. It starts with systems of linear equations and grows into the study of matrices, vector spaces, linear independence, dimension, linear transformations, orthogonality and projections, eigenvectors, and their applications. The resulting linear algebraic framework is a flexible and powerful way to approach multidimensional problems. Prerequisite(s): MATH 279 or MATH 137, or with permission of instructor, MATH 135 .

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Discrete mathematics studies collections of distinct, separate objects and is complementary to calculus (which studies continuous phenomena). This course introduces techniques for analyzing arrangements of objects and the relationships between them. The material emphasizes problem solving and logical argumentation, rather than computation. Topics include basic counting principles, induction, logic, recurrence relations, number theory, and graph theory.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Discrete mathematics studies collections of distinct, separate objects and is complementary to calculus (which studies continuous phenomena). This course introduces techniques for analyzing arrangements of objects and the relationships between them. The material emphasizes problem solving and logical argumentation, rather than computation. Topics include basic counting principles, induction, logic, recurrence relations, number theory, and graph theory.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Introduction to the theory and application of differential equations. Solving linear and first-order systems using algebra, linear algebra, and complex numbers. Using computers to solve equations both symbolically and numerically and to visualize the solutions. Qualitative methods for nonlinear dynamical systems. Applications to diverse areas of modeling. Prerequisite(s): MATH 236 and MATH 237.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

An introduction to probability theory and application. Fundamental probability concepts include: sample spaces, combinatorics, conditional probability, independence, random variables, probability distributions, expectation, variance, moment-generating functions, and limit theorems. Special course topics vary and may include: computer simulation, stochastic processes, and statistical inference. Prerequisite(s): MATH 237; or MATH 137 and MATH 236 .

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

A course in the study of functions of complex numbers, a topic which touches fields as varied as number theory, applied mathematics, physics, engineering, algebraic geometry, and more. We cover: geometry and algebra of complex numbers; complex functions; differentiation and integration, including the Cauchy­Riemann equations, Cauchy's theorem, and the Cauchy integral formula; Taylor series, Laurent series, and the Residue Theorem. Throughout, we emphasize complex functions as transformations of the plane, and also make a strong connection to applications. This course is appropriate both for students with an interest and background in theoretical mathematics and proof, and students whose primary interest is the application of mathematics to other fields. Prerequisite(s): MATH 236 and MATH 237.

General Education Requirements:

Distribution Requirements:

Course Materials

An important course for students considering graduate work in statistics or biostatistics, this course explores the mathematics underlying modern statistical applications. Topics include: classical techniques for parameter estimation and evaluation of estimator properties, hypothesis testing, confidence intervals, and linear regression. Special topics vary and may include: tests of independence, resampling techniques, introductory Bayesian concepts, and non­parametric methods. Though not the focus of this course, concepts will be highlighted through applications in a variety of settings. Prerequisite(s): MATH 354 .

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

A course in both theoretical and computational mathematics. Theoretical concepts include fundamental ideas from point set topology---continuity, convergence, and connectedness---as well as selected topics from algebraic topology---the fundamental group, elementary homotopy theory, and homology. This theoretical framework provides a backbone to understand new advances in topological data analysis. Applications are chosen from diverse fields such as biological aggregations, medicine, image processing, signal processing, and sensor networks. This course counts towards the capstone requirement. Prerequisite(s): MATH 365 or MATH 376 or MATH 377 .

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for applied work in the natural and social sciences. There is a strong emphasis on developing scientific computing and mathematical modeling skills. The topics include functions as models of data, differential calculus of functions of one and several variables, integration, differential equations, and estimation techniques. Applications are drawn from varied areas, including biology, chemistry, economics, and physics.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for applied work in the natural and social sciences. There is a strong emphasis on developing scientific computing and mathematical modeling skills. The topics include functions as models of data, differential calculus of functions of one and several variables, integration, differential equations, and estimation techniques. Applications are drawn from varied areas, including biology, chemistry, economics, and physics.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for both theoretical and applied work in the mathematical, natural, and social sciences. Topics include: partial derivatives, gradients, contour plots, constrained and unconstrained optimization, Taylor polynomials, interpretations of integrals via finite sums, the fundamental theorem of calculus, double integrals over a rectangle,and differential equations. Attention is given to both symbolic and numerical computing. Prerequisite(s): MATH 135 or a year of high school calculus at the level of AP calculus with an AB score of 4 or higher.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for the mathematical and physical sciences. Topics include: scalar and vector-valued functions and derivatives; parameterization and integration over regions, curves, and surfaces; the divergence theorem; and Taylor series. Attention is given to both symbolic and numerical computing. Applications drawn from the natural sciences, probability, and other areas of mathematics. Prerequisite(s): MATH 137 or a strong high school calculus at the level of AP calculus with a BC score of 4 or higher.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for the mathematical and physical sciences. Topics include: scalar and vector-valued functions and derivatives; parameterization and integration over regions, curves, and surfaces; the divergence theorem; and Taylor series. Attention is given to both symbolic and numerical computing. Applications drawn from the natural sciences, probability, and other areas of mathematics. Prerequisite(s): MATH 137 or a strong high school calculus at the level of AP calculus with a BC score of 4 or higher.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Discrete mathematics studies collections of distinct, separate objects and is complementary to calculus (which studies continuous phenomena). This course introduces techniques for analyzing arrangements of objects and the relationships between them. The material emphasizes problem solving and logical argumentation, rather than computation. Topics include basic counting principles, induction, logic, recurrence relations, number theory, and graph theory.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course examines the theoretical foundations of computation. It explores different mathematical models that try to formalize our informal notion of an algorithm. Models include finite automata, regular expressions, grammars, and Turing machines. The course also discusses ideas about what can and cannot be computed. In addition, the course explores the basics of complexity theory, examining broad categories of problems and their algorithms, and their efficiency. The focus is on the question of P versus NP, and the NP-complete set. Prerequisite(s): (COMP 128 or COMP 221) and MATH 279, or permission of instructor.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

A mix of applied linear algebra and numerical analysis, this course covers a central point of contact between mathematics and computer science. Many of the computational techniques important in science, commerce, and statistics are based on concepts from linear algebra, such as subspaces, projections, and matrix decompositions. The course reviews these concepts, adopts them to large scales, and applies them in the core techniques of scientific computing. These include solving systems of linear and nonlinear equations, approximation and statistical function estimation, optimization, interpolation, eigenvalue and singular value decompositions, and compression. Applications throughout the natural sciences, social sciences, statistics, and computer science Prerequisite(s): COMP 120 or COMP 123, and MATH 236

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

A mix of applied linear algebra and numerical analysis, this course covers a central point of contact between mathematics and computer science. Many of the computational techniques important in science, commerce, and statistics are based on concepts from linear algebra, such as subspaces, projections, and matrix decompositions. The course reviews these concepts, adopts them to large scales, and applies them in the core techniques of scientific computing. These include solving systems of linear and nonlinear equations, approximation and statistical function estimation, optimization, interpolation, eigenvalue and singular value decompositions, and compression. Applications throughout the natural sciences, social sciences, statistics, and computer science Prerequisite(s): COMP 120 or COMP 123, and MATH 236

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Introduction to algebraic structures, including groups, rings, fields, and vector spaces. Other topics may include geometric constructions, symmetry groups, algebraic coding theory, Burnside's counting theorem, Galois theory. Prerequisite(s): MATH 279 and MATH 236 .

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Linear algebra is one of the pillars of mathematics, both pure and applied. Linear relations can be used to model phenomena from numerous disciplines in the mathematical sciences, physical sciences, social sciences, engineering, and computer science. This introduction to linear algebra blends mathematical computation, theory, abstraction, and application. It starts with systems of linear equations and grows into the study of matrices, vector spaces, linear independence, dimension, linear transformations, orthogonality and projections, eigenvectors, and their applications. The resulting linear algebraic framework is a flexible and powerful way to approach multidimensional problems. Prerequisite(s): MATH 279 or MATH 137, or with permission of instructor, MATH 135 .

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Discrete mathematics studies collections of distinct, separate objects and is complementary to calculus (which studies continuous phenomena). This course introduces techniques for analyzing arrangements of objects and the relationships between them. The material emphasizes problem solving and logical argumentation, rather than computation. Topics include basic counting principles, induction, logic, recurrence relations, number theory, and graph theory.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for applied work in the natural and social sciences. There is a strong emphasis on developing scientific computing and mathematical modeling skills. The topics include functions as models of data, differential calculus of functions of one and several variables, integration, differential equations, and estimation techniques. Applications are drawn from varied areas, including biology, chemistry, economics, and physics.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for applied work in the natural and social sciences. There is a strong emphasis on developing scientific computing and mathematical modeling skills. The topics include functions as models of data, differential calculus of functions of one and several variables, integration, differential equations, and estimation techniques. Applications are drawn from varied areas, including biology, chemistry, economics, and physics.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for applied work in the natural and social sciences. There is a strong emphasis on developing scientific computing and mathematical modeling skills. The topics include functions as models of data, differential calculus of functions of one and several variables, integration, differential equations, and estimation techniques. Applications are drawn from varied areas, including biology, chemistry, economics, and physics.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for both theoretical and applied work in the mathematical, natural, and social sciences. Topics include: partial derivatives, gradients, contour plots, constrained and unconstrained optimization, Taylor polynomials, interpretations of integrals via finite sums, the fundamental theorem of calculus, double integrals over a rectangle,and differential equations. Attention is given to both symbolic and numerical computing. Prerequisite(s): MATH 135 or a year of high school calculus at the level of AP calculus with an AB score of 4 or higher.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for both theoretical and applied work in the mathematical, natural, and social sciences. Topics include: partial derivatives, gradients, contour plots, constrained and unconstrained optimization, Taylor polynomials, interpretations of integrals via finite sums, the fundamental theorem of calculus, double integrals over a rectangle,and differential equations. Attention is given to both symbolic and numerical computing. Prerequisite(s): MATH 135 or a year of high school calculus at the level of AP calculus with an AB score of 4 or higher.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for both theoretical and applied work in the mathematical, natural, and social sciences. Topics include: partial derivatives, gradients, contour plots, constrained and unconstrained optimization, Taylor polynomials, interpretations of integrals via finite sums, the fundamental theorem of calculus, double integrals over a rectangle,and differential equations. Attention is given to both symbolic and numerical computing. Prerequisite(s): MATH 135 or a year of high school calculus at the level of AP calculus with an AB score of 4 or higher.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Linear algebra is one of the pillars of mathematics, both pure and applied. Linear relations can be used to model phenomena from numerous disciplines in the mathematical sciences, physical sciences, social sciences, engineering, and computer science. This introduction to linear algebra blends mathematical computation, theory, abstraction, and application. It starts with systems of linear equations and grows into the study of matrices, vector spaces, linear independence, dimension, linear transformations, orthogonality and projections, eigenvectors, and their applications. The resulting linear algebraic framework is a flexible and powerful way to approach multidimensional problems. Prerequisite(s): MATH 279 or MATH 137, or with permission of instructor, MATH 135 .

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Linear algebra is one of the pillars of mathematics, both pure and applied. Linear relations can be used to model phenomena from numerous disciplines in the mathematical sciences, physical sciences, social sciences, engineering, and computer science. This introduction to linear algebra blends mathematical computation, theory, abstraction, and application. It starts with systems of linear equations and grows into the study of matrices, vector spaces, linear independence, dimension, linear transformations, orthogonality and projections, eigenvectors, and their applications. The resulting linear algebraic framework is a flexible and powerful way to approach multidimensional problems. Prerequisite(s): MATH 279 or MATH 137, or with permission of instructor, MATH 135 .

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for the mathematical and physical sciences. Topics include: scalar and vector-valued functions and derivatives; parameterization and integration over regions, curves, and surfaces; the divergence theorem; and Taylor series. Attention is given to both symbolic and numerical computing. Applications drawn from the natural sciences, probability, and other areas of mathematics. Prerequisite(s): MATH 137 or a strong high school calculus at the level of AP calculus with a BC score of 4 or higher.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

This course focuses on calculus useful for the mathematical and physical sciences. Topics include: scalar and vector-valued functions and derivatives; parameterization and integration over regions, curves, and surfaces; the divergence theorem; and Taylor series. Attention is given to both symbolic and numerical computing. Applications drawn from the natural sciences, probability, and other areas of mathematics. Prerequisite(s): MATH 137 or a strong high school calculus at the level of AP calculus with a BC score of 4 or higher.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Discrete mathematics studies collections of distinct, separate objects and is complementary to calculus (which studies continuous phenomena). This course introduces techniques for analyzing arrangements of objects and the relationships between them. The material emphasizes problem solving and logical argumentation, rather than computation. Topics include basic counting principles, induction, logic, recurrence relations, number theory, and graph theory.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Discrete mathematics studies collections of distinct, separate objects and is complementary to calculus (which studies continuous phenomena). This course introduces techniques for analyzing arrangements of objects and the relationships between them. The material emphasizes problem solving and logical argumentation, rather than computation. Topics include basic counting principles, induction, logic, recurrence relations, number theory, and graph theory.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Discrete mathematics studies collections of distinct, separate objects and is complementary to calculus (which studies continuous phenomena). This course introduces techniques for analyzing arrangements of objects and the relationships between them. The material emphasizes problem solving and logical argumentation, rather than computation. Topics include basic counting principles, induction, logic, recurrence relations, number theory, and graph theory.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

Introduction to the theory and application of differential equations. Solving linear and first-order systems using algebra, linear algebra, and complex numbers. Using computers to solve equations both symbolically and numerically and to visualize the solutions. Qualitative methods for nonlinear dynamical systems. Applications to diverse areas of modeling. Prerequisite(s): MATH 236 and MATH 237.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

An introduction to probability theory and application. Fundamental probability concepts include: sample spaces, combinatorics, conditional probability, independence, random variables, probability distributions, expectation, variance, moment-generating functions, and limit theorems. Special course topics vary and may include: computer simulation, stochastic processes, and statistical inference. Prerequisite(s): MATH 237; or MATH 137 and MATH 236 .

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

An introduction to probability theory and application. Fundamental probability concepts include: sample spaces, combinatorics, conditional probability, independence, random variables, probability distributions, expectation, variance, moment-generating functions, and limit theorems. Special course topics vary and may include: computer simulation, stochastic processes, and statistical inference. Prerequisite(s): MATH 237; or MATH 137 and MATH 236 .

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Basic theory for the real numbers and the notions of limit, continuity, differentiation, integration, convergence, uniform convergence, and infinite series. Additional topics may include metric and normed linear spaces, point set topology, analytic number theory, Fourier series. Prerequisite(s): MATH 237.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

A second course in discrete mathematics that develops more advanced counting techniques. Combinatorics is the study of arrangements, patterns and configurations. Generally speaking,  we fix a set of objects and then arrange those objects into patterns satisfying special rules. Once we identify an interesting family of objects, we ask: how many are there? what are their structural properties? how can we find the "best" one(s)?  Topics are drawn from  graph theory, enumerative combinatorics, graph algorithms, and generating functions. Prerequisite(s): MATH 279 and MATH 237 .

General Education Requirements:

Distribution Requirements:

Course Materials

Topics in applied mathematics chosen from: Fourier analysis; partial differential equations; wavelets; signal processing; time-frequency analysis; stochastic processes; optimization; computational geometry; and more. Topics are examined in theoretical and applied contexts, and from analytical and computational viewpoints. This course counts toward the capstone requirement. May be repeated for credit with departmental approval. Prerequisite(s): MATH 236 and one of the following: COMP 120 or COMP 123 or COMP 124. MATH 312 or MATH 365 recommended.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

A course in matrix representations of groups, a topic which unites the powers of group theory and linear algebra. Topics include: symmetry in linear spaces, modules, group actions, characters, tensor products, and Fourier analysis on groups. Applications are chosen from: ranked data, molecular vibrations, quantum mechanics, random walks, number theory, and combinatorics. Important ideas from linear algebra are revisited from a more sophisticated point of view. These include: linear transformations, abstract vector spaces, change of basis, subspaces, direct sums, projections, and eigenvalues and eigenvectors. Prerequisite(s): MATH 376 .

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials