Mathematics Classes

A first course designed for students with no previous calculus experience. 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

A first course designed for students with no previous calculus experience. 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

A first course designed for students with no previous calculus experience. 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

A second course in calculus that focuses on theoretical and applied calculus 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 AP Calculus AB (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 5), or IB HL Mathematics: Applications & Interpretations (with a score of 6 or 7), or a comparable year of high school calculus.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

A second course in calculus that focuses on theoretical and applied calculus 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 AP Calculus AB (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 5), or IB HL Mathematics: Applications & Interpretations (with a score of 6 or 7), or a comparable year of high school calculus.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

A second course in calculus that focuses on theoretical and applied calculus 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 AP Calculus AB (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 5), or IB HL Mathematics: Applications & Interpretations (with a score of 6 or 7), or a comparable year of high school calculus.

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 STAT 155.

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 STAT 155.

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 STAT 155.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

A third course in calculus that focuses on methods 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 AP Calculus BC (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 6 or 7), or a comparable two years of high school calculus.

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

A survey of differential equations as a tool for the study of smoothly varying quantities, with applications ranging from the physical sciences (e.g. radioactive decay and mechanics) to human behavior (e.g. economics and linguistics). We introduce famous scalar and vector differential equations as modeling tools. We cover standard analytical, computational, and qualitative methods for studying differential equations. Further topics can include the Laplace transform, an introduction to partial differential equations, dynamical systems, specialized applications, or rigorous existence and uniqueness theorems. Prerequisite(s): MATH 236 and MATH 237.

General Education Requirements:
Writing WP

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 137 or MATH 237

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

An important course for students considering graduate work in statistics or biostatistics, this course explores the mathematical theory underlying modern statistical techniques. Topics include the theory behind: parameter estimation, 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. Prerequisite(s): STAT 155, MATH 236, MATH 354/STAT 354.

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): MATH 236; one of: MATH 135 or MATH 137 or MATH 237 ; one of: COMP 120 or COMP 123 or COMP 127 or COMP 128; 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): MATH 236; one of: MATH 135 or MATH 137 or MATH 237 ; one of: COMP 120 or COMP 123 or COMP 127 or COMP 128; or permission of instructor.

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

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

General Education Requirements:

Distribution Requirements:

Course Materials

A continuation of Real Analysis. Topics chosen from: the development of the Riemann and Lebesgue integrals; measure theory; functional analysis; Fourier analysis. A large component of the course will be an open-ended exploratory project. This course counts toward the capstone requirement. Prerequisite(s): MATH 236 and MATH 377

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

The modern Information Age has produced a wealth of data about the complex networks that tie us together. In response, the field of Network Science has arisen, bringing together mathematics, computer science, sociology, biology, economics and other fields. This course will explore the fundamental questions and the mathematical tools of Network Science. This includes: the structure of complex networks, including connectedness, centrality and "long tails"; community detection; random/strategic models for network formation; diffusion/contagion and "tipping points" on networks; and algorithms for analyzing complex networks. Prerequisite(s): COMP 123, MATH 236, MATH 279 and one of: COMP 221, MATH 354/STAT 354, MATH 375, or MATH 379.

General Education Requirements:
Quantitative Thinking Q2

Distribution Requirements:
Natural science and mathematics

Course Materials

A first course designed for students with no previous calculus experience. 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

A first course designed for students with no previous calculus experience. 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

A first course designed for students with no previous calculus experience. 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

A second course in calculus that focuses on theoretical and applied calculus 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 AP Calculus AB (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 5), or IB HL Mathematics: Applications & Interpretations (with a score of 6 or 7), or a comparable year of high school calculus.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

A second course in calculus that focuses on theoretical and applied calculus 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 AP Calculus AB (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 5), or IB HL Mathematics: Applications & Interpretations (with a score of 6 or 7), or a comparable year of high school calculus.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

A second course in calculus that focuses on theoretical and applied calculus 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 AP Calculus AB (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 5), or IB HL Mathematics: Applications & Interpretations (with a score of 6 or 7), or a comparable year of high school calculus.

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 STAT 155.

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 STAT 155.

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 STAT 155.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

A third course in calculus that focuses on methods 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 AP Calculus BC (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 6 or 7), or a comparable two years of high school calculus.

General Education Requirements:
Quantitative Thinking Q1

Distribution Requirements:
Natural science and mathematics

Course Materials

A third course in calculus that focuses on methods 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 AP Calculus BC (with a score of 4 or 5), or IB HL Mathematics: Analysis & Approaches (with a score of 6 or 7), or a comparable two years of high school calculus.

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

A survey of differential equations as a tool for the study of smoothly varying quantities, with applications ranging from the physical sciences (e.g. radioactive decay and mechanics) to human behavior (e.g. economics and linguistics). We introduce famous scalar and vector differential equations as modeling tools. We cover standard analytical, computational, and qualitative methods for studying differential equations. Further topics can include the Laplace transform, an introduction to partial differential equations, dynamical systems, specialized applications, or rigorous existence and uniqueness theorems. Prerequisite(s): MATH 236 and MATH 237.

General Education Requirements:
Writing WP

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 137 or 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 137 or MATH 237

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Graphs are mathematical structures which represent the relationships between objects in a set. Graph Theory falls under the umbrella of discrete mathematics and borrows methods from several areas of study to explore properties like the overall strength and complexity of the graph. Topics in this course include connectivity, graph coloring, trees, graph algorithms, and network flows. This course also discusses how these topics relate to graphs found in applications, such as social networks and the internet. Prerequisite(s): MATH 279

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 137 and one of: MATH 236, MATH 237, or MATH 279.

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 137 and one of: MATH 236, MATH 237, or MATH 279.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Partial differential equations are powerful tools for modeling and simulation, with wide use in science and engineering. This course introduces some famous and well-understood equations (e.g. for modeling heat flow, waves, advection, and gravitation) and covers strategies for solving them on paper and by machine; applications in one, two and three space dimensions are covered. Nonlinear equations are introduced more briefly. Capstone projects allow students to apply or extend their knowledge to a problem of their choice. Prerequisite(s): MATH 312

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Discrete optimization applies techniques from combinatorics and graph theory, along with algorithmic thinking, to find the best solution to problems with finite structures. This course introduces the integer program as a powerful tool to solve these problems before diving into more specialized methods for canonical problems, including maximizing flow in a network, finding shortest paths, and creating optimal schedules. Spanning both theory and applied, this course develops both proofs of correctness for these solutions and methods of implementation with code. Students will apply or extend their knowledge of the area with a capstone project on the problem of their choice. Prerequisite(s): Math 236, Comp 123 (or above), and one of the following: Math 375 or Math 379, or permission of the instructor.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials