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:

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.STAT Prerequisite(s): STAT 155, MATH 236, MATH 354/STAT 354.

General Education Requirements:

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): MATH 236 and one of: COMP 120 or COMP 123 or COMP 127 or COMP 128.

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 and one of: COMP 120 or COMP 123 or COMP 127 or COMP 128.

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 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:
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 236 and one of: MATH 365; or MATH 375; or MATH 376; or MATH 377; or MATH 378; or MATH 379.

General Education Requirements:

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

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

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

This course provides an introduction to the representation theory of quivers—directed graphs that serve as a combinatorial framework for studying linear algebraic structures. Topics may include path algebras, indecomposability, projectivity and injectivity of representations, Dynkin diagrams, classes of quivers, Gabriel’s theorem, and Auslander-Reiten theory. Important background knowledge from algebra and category theory will be introduced as necessary. We will also explore applications of quiver representations in areas such as topological data analysis (TDA), theoretical physics, neural networks, and chemical reactions networks. Prerequisite(s): MATH 236

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Draws on the student's general background in mathematics to construct models for problems arising from such diverse areas as the physical sciences, life sciences, political science, economics, and computing. Emphasis will be on the design, analysis, accuracy, and appropriateness of a model for a given problem. Case studies will be used extensively. Specific mathematical techniques will vary with the instructor and student interest. This course counts towards the capstone requirement. Prerequisite(s): MATH 312 and one of the following:  COMP 120 or COMP 123 or COMP 124.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials

Computational and discrete geometry is the study of geometric objects and algorithms for problems involving geometric input and output. It originally developed as a generalization of the study of algorithms for sorting and searching in 1-dimensional space to problems involving multi-dimensional inputs. Topics will likely include: polygons and polyhedra, convex hulls, Voronoi diagrams, triangulations, medial axis, linear optimization, search algorithms, and configuration spaces. This is a course in both theoretical and computational mathematics. Students will understand and apply definitions, work out examples both by hand and using a computer, investigate algorithms, and apply the tools learned in the class to a variety of applications. Coursework will involve problem sets, at least one exam (likely take-home), and a final project that includes a paper and presentation. An exploration of research articles and relevant literature will be a component of the course as well.

General Education Requirements:

Distribution Requirements:
Natural science and mathematics

Course Materials