Undergraduate Mathematics course descriptions and syllabi by semester. Scroll down or use the search function to the right to find your course.
MATH 101 – Math in the Social Sciences
The course is primarily focused on using mathematics to solve a range of practical, real-world problems, including problems of specific interest to those in the social sciences. Many relevant and interesting questions can be answered without complex algebraic manipulations, and in this course we develop the tools to solve some of these problems. For example:
- How can different voting methods be used to determine the outcome of an election?
- How are seats in the US House of Representatives currently apportioned, and how has this been done historically?
- How can a collection of assets be fairly divided among a group of people?
- How can delivery drivers be routed to deliver packages quickly and efficiently?
- How can a traveling salesman minimize travel time on a business trip to several cities?
MATH 105 – Patterns of Phenomena
Applications of mathematical ideas and mode of thought in the arts and humanities, focusing on classification, recognition.
MATH 116/117/118 – Precalculus Supplement for Success in Math/College Algebra in Context I/ College Algebra in Context II
116: Supplemental academic instruction developing skills to succeed in precalculus courses and future mathematics and STEM courses.
117: Functions as mathematical models. Linear, quadratic, and polynomial functions considered symbolically, graphically, numerically, and contextually.
118: Reciprocals of linear functions, rational functions, and power functions considered symbolically, graphically, numerically, and contextually.
Select Syllabi
MATH 120 – College Algebra
The world we live in is full of varying quantities: the amount of time passed since a certain event, how much profit a company makes throughout a year, the growing or shrinking population of a town, and even the distance you travel around campus throughout the day. The techniques of college algebra allow us to examine how these varying quantities change, and how they change together. We are even able to create formulas to calculate exactly how something like a population can change as time passes.
In this class, we will develop formulas and functions that represent quantities that vary with a constant rate of change (linear functions), those that vary with a constant percent change (exponential functions), and those that are best represented with polynomial functions. Throughout the class, we will focus on the language used to explain how quantities change together in order to better understand the world around us. We will develop an understanding of function notation, interpret vertical and horizontal intercepts, and even how to invert and compose functions to create even more useful functions.
MATH 127 – Precalculus
The world we live in is full of varying quantities: the amount of time passed since a certain event, how much profit a company makes throughout a year, the growing or shrinking population of a town, and even the distance you travel around campus throughout the day. The techniques of precalculus allow us to examine how these varying quantities change, and how they change together. We are even able to create formulas to calculate exactly how something like a population can change as time passes.
In this class, we will develop formulas and functions that represent quantities that vary with a constant rate of change (linear functions), those that vary with a constant percent change (exponential functions), those that are best represented with polynomial or a rational functions, and those that best represent an object moving along a circular path (trigonometric functions). Throughout the class, we will focus on the language used to explain how quantities change together in order to better understand the world around us. We will develop an understanding of function notation, interpret vertical and horizontal intercepts, and even how to invert and compose functions to create even more useful functions. In order to prepare for calculus, we will also look at the limits of functions and delve into what it means to approach infinity.
MATH 141 – Calculus in Management Sciences
Analytic geometry, limits, equilibrium of supply and demand, differentiation, integration, applications of the derivative, integral.
MATH 151 – Mathematical Algorithms in Matlab
Statements, expressions and variable assignments, scripts, control statements and logical statements. Newton’s method, Simpson’s rule, recursion.
MATH 155 – Calculus for Biological Scientists
Limits, continuity, differentiation, and integration of elementary functions with applications in the biosciences.
MATH 156 – Mathematics for Computational Science
MATH 156 is a first college mathematics class for Computer Science majors. It is split, about half in foundational material (sets, equivalence relations, functions, sequences and series) and half in a survey of 1-dimensional Calculus. For this second part the focus is on applications relevant to Computer and Data Science (Optimization, Newton’s method, Order of Growth, Taylor approximations), rather than on applications in the physical sciences or in showing fluency in calculating (anti)derivatives. There is no mention of differential equations. Limits and continuity are considered more informally than they are in other calculus courses.
This class is useful for students with interests in computation and data, but who do not aim for modeling of physical phenomena. It might not be sufficient preparation for MATH 161, 255, or 271, and for Mathematics majors it is only suitable in the Computational Mathematics concentration.
MATH 160 – Calculus for Physical Scientists I
Limits, continuity, differentiation, and integration of trigonometric and transcendental functions with applications.
The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Connections among representations are also emphasized.
Upon the completion of this course, students will be able to:
- Evaluate limits using appropriate analytical, numerical, or graphical techniques.
- Analyze the continuity of functions.
- Apply the definition and techniques of differentiation to find derivatives including derivatives of transcendental functions.
- Analyze functions represented by an equation or a graph using derivatives and limits.
- Create graphs of functions using properties of derivatives, limits, and integrals.
- Apply techniques of integration to find antiderivatives of a function.
- Evaluate definite integrals using Riemann sums, the Fundamental Theorem of Calculus,
- geometry, and technology.
- Utilize calculus techniques to solve application problems.
- Apply mathematical definitions and construct logical arguments.
MATH 161 – Calculus II
This course builds both the problem solving skills and the mathematical toolbox required for tackling single variable problems in contemporary applied math, physics, engineering, mathematical modeling, and data science. The first half of the course is concerned with integrals – methods of evaluation and applications – and the second half of the course develops Taylor series, an often indispensible tool in areas of math such as differential equations and numerical methods, culminating in a brief introduction to the complex number system.
Analyzing mathematical situations is key, and being able to think through a problem, understand what it is going on, draw a diagram if necessary, and make appropriate mathematical choices is essential for success. A firm practical foundation in precalculus and calculus 1, including a computational fluency appropriate for the level of the course, is expected.
MATH 192 – First-Year Experience in Mathematics
Introduction to the richness and variety of problems addressed by mathematical language and techniques; resources and available careers.
MATH 229 – Matrices & Linear Equations
Linear systems, matrix arithmetic, homogeneous coordinates, complex numbers, eigenvalues, eigenvectors, applications to discrete dynamical systems.
Select Syllabi
MATH 230 – Discrete Mathematics for Educators
Voting theory, fair division, graph theory, linear programming, probability, teaching in small groups, proof techniques, mathematical technology.
Select Syllabi
MATH 235 – Introduction to Mathematical Reasoning
This class is intended to help the transition from lower division mathematical courses, mostly based on procedures and algorithms, to upper division courses, where several skills of induction, deduction and logical thinking are necessary to understand, explain, and prove mathematical statements. Among these skills are understanding and using definitions; understanding implications; learning what it means to prove a mathematical statement and how to write elementary proofs; and appreciating the importance of examples and counterexamples in the understanding and development of mathematics. This class is meant to develop a number of skills that are important for practicing mathematics.
For this course the journey is much more important than the destination; each professor teaching the course chooses to illustrate and train these skills via mathematical topics that are closest to their heart. Topics that have been used in recent years include combinatorics, convex geometry, discrete mathematics, elementary number theory, and topology.
Select Syllabi
MATH 255 – Calculus for Biological Scientists II
Derivatives and integrals of functions of several variables, differential and difference equations, matrices, applications in the biosciences.
MATH 256 – Mathematics for Computational Science II
Methods from vector calculus, advanced calculus, and analytic geometry are relevant to machine learning and data science, enabling one to determine various properties of data sets, train machine learning algorithms, and more. Further, some of these concepts are integral to a deeper understanding of statistics.
The course starts with topics from univariate integral theory with a focus on applications to probability and image processing: convolutions, improper integrals, and probability distributions. Concepts from multivariate calculus include multivariate and vector-valued functions; partial derivatives, gradients, and Taylor series; and multivariate integration with an eye towards optimization. Finally, an introduction to surfaces and manifolds will be used to understand the shape of data sets, and l^p norms will be discussed as a tool in regularization.
Select Syllabi
MATH 261 – Calculus III
This course covers multivariable and vector calculus. It extends the concepts of derivative and integral introduced in single-variable calculus to partial derivative, directional derivative, and double/triple integrals, line and surface integrals. The detailed topics include vectors, parametric curves; Surfaces in three-dimension, partial derivatives and chain rule, gradient vectors and directional derivative; Application of differentiation (linear approximation, Lagrange multipliers for constrained optimization); Double and triple integrals in different coordinate systems; Vector fields, line integrals and flux integrals of vector-valued functions. At the end, integration theorems (Green’s theorem, Stokes’ theorem and divergence theorem) are introduced that generalize the Fundamental Theorem of Calculus to higher dimensions.
Prerequisites: The prerequisites for this course are Calculus I and Calculus II, and a thorough understanding of the topics covered in that course is essential for succeeding in Calculus III.
Select Syllabi
MATH 269 – Geometric Introduction to Linear Algebra
Geometric interpretations in ℝ² and ℝ³ of core linear algebra concepts including vector spaces, matrices, linear transformations, span, basis, and linear independence with applications. This course will focus on linear algebra concepts but only in ℝ² and ℝ³. Students will have opportunities to engage with the concepts in physical environments and through technology, before being introduced to the symbolism and formalism. The goal of these activities is to help the students ground the concepts and make sense of the computations in ℝ² and ℝ³, so that they are better prepared to work with concepts in higher dimensions. The goals for the course are:
- perform computations required for linear algebra,
- develop geometric interpretations of linear algebra computations, and
- apply and connect linear algebra to meaningful contexts outside of the mathematics classroom.
MATH 271 – Applied Mathematics for Chemists I
Series and limits, Taylor series, complex variables, first- and second- order ordinary differential equations, matrices, linear transformations, determinants, and eigenvalues.
Select Syllabi
MATH 272 – Applied Mathematics for Chemists II
Vector fields, partial differentiation, cylindrical and spherical coordinates, multiple integrals, line integrals, the Wave and the Schrödinger equations, separation of variables method. Inner Product Spaces. Fourier Series.
Select Syllabi
MATH 301 – Introduction to Combinatorial Theory
Combinatorics is the mathematical theory of counting, connection, and combinations.
A primary theme in combinatorics is to construct and enumerate discrete configurations and structures, and answer questions about the existence and optimizations of these. This field has roots that emerged in ancient civilizations and continues to gain new applications in many other areas, including computer science and operations research.
This course covers key topics in combinatorics, including enumeration, combinatorial proof techniques, and graph theory. Topics in enumeration include: counting principles (sequences, permutations, and (multi) sets), inclusion-exclusion, Pascal’s triangle, the binomial theorem, recurrence relations, and generating functions. Topics covered in graph theory include: walks, circuits, trees, matchings, optimizations, planarity, and coloring.
MATH 317 – Advanced Calculus of One Variable
Convergence of sequences, series: limits, continuity, differentiation, integration of one-variable functions.
MATH 331 – Introduction to Mathematical Modeling
Problem formulation. Modeling, theoretical and empirical. Variable selection. Derivation and simulation of solutions. Model testing including prediction.
Select Syllabi
MATH 332 – Partial Differential Equations
This course explores partial differential equations (PDEs), which arise when phenomena
involving two or more dimensions are modeled mathematically: how does a fluid flow,
how does a solid deform, how is heat transported within a body, how do waves
propagate in matter?
We classify PDEs as elliptic, parabolic, and hyperbolic and develop techniques to
analytically solve problems in each category. Like most practical differential equations,
PDEs generally cannot be solved by deriving a formula, and we often cannot even express
a solution in the form of an infinite series, but solutions can be found in special
cases, and these provide insight into more general solution approaches (analytic or
numeric). When a solution cannot be found, we may still be able to determine properties
a solution must have (such as smoothness or regularity).
Select Syllabi
MATH 340 – Intro to Ordinary Differential Equations
First and second order equations, series, Laplace transforms, linear algebra, eigenvalues, first order systems of equations, numerical techniques.
MATH 345 – Differential Equations
This course provides an introduction to differential equations, which arise in many situations in science and engineering. The course begins with first-order equations, describing theory and
solution techniques, explores numerical methods of approximating solutions, and presents a variety of applications. It then covers linear second-order equations and techniques including the methods of undetermined coefficients and variation of parameters, with several real-world applications. It describes how infinite series can be used to find solutions, and discusses the Laplace transform and convolution methods to handle impulses and discontinuous functions.
The course briefly explores higher-order equations, extending the methods introduced for second-order, and finally, examines how to apply eigenvalue techniques from linear algebra to solve systems of linear differential equations.
MATH 348 – Theory of Population and Evolutionary Ecology
The principal objective of this course is to familiarize students with the theory of population and evolutionary ecology. Students will gain enough background to read theoretical population and evolutionary ecology literature, do simple modeling, and springboard to more complex theory if desired. This course is a strong mix of mathematics and ecology. The students in the course typically have some knowledge in one of these areas (for example, calculus and linear algebra from mathematics; or ecology and evolution from the biological side). Few students will have strong experience in both and some students have the prerequisite calculus and no ecology. We work with all backgrounds to develop new skills, knowledge and understanding throughout the semester. The goal is to learn about theoretical ecology and begin to create models. The learning curve is steep early in the semester and diligence and patience will pay off.
Select Syllabi
MATH 350 – Numerical Analysis I
This course provides an introduction to the basic techniques in this area, covering specifically “discrete
problems” such as the solution of linear and nonlinear systems, matrix decompositions, and eigenvalue
problems. These techniques will re-appear as the building blocks of more complicated algorithms, such as
those we consider in Numerical Analysis II (MATH 450).
Select Syllabi
MATH 360 – Mathematics of Information Security
The main topic of information security is cryptosystems, which are designed to protect secret information, including banking, communication, and storage data. For 50 years, people have benefitted from the ability to transmit private information over public channels because of public key cryptography. Many public key cryptosystems rely on number theory, which is the study of patterns made by positive integers. See also this poster on the mathematics of information security from the National Academies: https://nap.nationalacademies.org/resource/other/deps/illustrating-math/interactive/pdf/Securing-the-internet.pdf
This course is focused on the mathematics underlying public key cryptosystems. To do this, the course develops key mathematical concepts in number theory, including modular arithmetic, units, primitive roots, and the theorems of Sun Ze, Fermat, and Euler. The main topics in cryptography include: public key ciphers, the El Gamal cryptosystem, the RSA cryptosystem, AES encryption, and primality testing. Other topics may include: finite fields, square roots, probabilistic encryption, and collision algorithms.
MATH 366 – Introduction to Abstract Algebra
The goal of abstract algebra is to study the algebraic structure shared by different types of sets, including the integers, polynomials, real and complex numbers, and matrices. This provides a powerful technique to analyze and prove results in many different situations.
This course is an introduction to the abstract algebra topics of groups, rings, and fields. Key topics for groups include orders of elements, Lagrange’s theorem, abelian groups, and permutation groups. Key topics for rings include units, zero-divisors, factorization, and ideals. An important technique is to study homomorphisms of groups (or rings) and the first isomorphism theorem. Additional topics will include some of the following: cosets, conjugation, normal subgroups, quotient groups; prime and maximal ideals, quotient rings, and extension fields.
MATH 369 – Linear Algebra I
Linear systems, matrices, subspaces of Euclidean spaces, linear transformations on Euclidean spaces, eigenvalues, eigenvectors.
Select Syllabi
MATH 384 – Supervised College Teaching
Skills for effective tutoring of precalculus mathematics; design and implementation of the Individualized Mathematics Program.
MATH 405 – Introduction to Number Theory
Number theory is a fascinating branch of mathematics, whose roots emerge in ancient civilizations and which includes famous problems like Fermat’s Last Theorem and the Riemann hypothesis. The underlying concept in number theory is to study solutions to equations whose values are integers and to investigate the behavior of prime numbers.
This course will cover important topics in number theory, including: Diophantine equations (e.g., Pell, Fermat); quadratic reciprocity; quadratic number fields; and distribution of prime numbers. Additional topics may include: finite fields, Gauss sums, prime number theorem, multiplicative functions, and elliptic curves.
Select Syllabi
MATH 417 – Advanced Calculus I
Topology of Euclidean spaces, limits, derivatives and integrals on Euclidean spaces. Implicit functions and the implicit function theorem.
MATH 419 – Introduction to Complex Variables
The complex numbers are a central topic in mathematics, connecting to almost every area and providing powerful tools and insight in combinatorics, geometry, number theory, and many others. While the complex numbers were originally defined for an algebraic purpose, namely to solve polynomial equations, this course explores their analytic aspects, starting with the definition of the complex derivative and exploring the many surprising ramifications of functions being complex-differentiable.
In contrast to functions which are differentiable over the real numbers, complex-differentiable functions–usually called holomorphic functions–can always be represented by power series. This leads to powerful structural and computational theorems, including Cauchy’s theorem, Liouville’s theorem, and the residue theorem, and fundamental connections with and applications to partial differential equations, analytic combinatorics and number theory, and topology.
Select Syllabi
MATH 425 – History of Mathematics
By a course on Mathematics we signify that we will be learning mathematics in this course as well as history. Using a historical development of mathematics, we will learn how pure and applied mathematics are intertwined. The study of how mathematics was developed can help us teach mathematics and thus, pedagogy will be part of the course. Student interests will influence the selected course topics. Goals for the course are for students to:
- examine mathematics through a historical lens, by solving familiar mathematical tasks using historical methods,
- explore how a historical lens of mathematics can inform your teaching, by reflecting and planning on how you will use this lens in your future classrooms,
- reflect on how mathematics is embedded in social and political contexts, by reading, reflecting, and writing about your new discoveries, and
- interact with a diverse set of mathematicians, by interviewing and listening to them.
Select Syllabi
MATH 430 – Fourier and Wavelet Analysis with Apps
The ideas of Fourier analysis are deeply embedded in many areas of science and engineering. The notions of Fourier analysis underlie even the names of subfields (e.g. “ultrawideband radar”), the basic tools on which further mathematical machinery is based (e.g., microlocal analysis), and questions of public policy (e.g., spectrum management, broadband access).
In this course you will gain a comprehensive theoretical understanding of the four Fourier transforms: the continuous-time Fourier transform, the continuous-time Fourier series, the discrete-time Fourier transform, and the discrete Fourier transform. You will understand and apply connections between these transforms along with sampling theorems and Poisson summation formulas. In addition, you will learn more general transforms, in particular the Gabor and wavelet transforms, and will be able to apply fast Fourier transform and wavelet algorithms to spectrum analysis, imaging, and compression of sound and image files.
This is a key course for students interested in data analysis, signal and image processing and information sciences.
MATH 435 – Projects in Applied Mathematics
Open-ended projects with emphasis on problem identification and formulation, team approach, and reporting results.
Select Syllabi
MATH 450 – 2024 Newly Revised: Numerical Analysis II
Numerical methods are employed to solve mathematical or engineering problems on
computers. They are typically formulated as algorithms which are sequences of steps that can be implemented
in various programming languages. Additionally, numerical analysis also deals with examining properties of
numerical methods, e.g. their performance. This introductory course covers the following topics:
- Solution of nonlinear equations f(x) = 0
- Solution of systems of linear equations Ax = b
- Interpolation: fitting functions through a set of data points
- Approximation: fitting functions to approximate a set of data points
The solution of ordinary and partial differential equations as well as eig
Select Syllabi
MATH 455 – Mathematics in Biology and Medicine
In this course, we will cover material including models in population biology, cell division, host-parasitoid systems, bacterial growth in a chemostat, and predator-prey systems. The mathematical topics include linear and nonlinear difference equations, in particular the logistic equation, continuous processes and ordinary differential equations, and stability considerations for both discrete and continuous models. We will also cover several techniques of medical imaging. The prerequisites for the course are two semesters of calculus and differential equations, which may be taken parallel to this course.
Select Syllabi
MATH 460 – Information and Coding Theory
The goal of coding theory is to provide a mathematical way to correct and compress data that is being stored or transmitted over a channel. The topic of information theory is to provide bounds on the ability to do so. This field developed in the 1940s with the work of Shannon and continues to grow because of new applications. It relies on several mathematical topics, including linear algebra, discrete math, and probability theory.
This course is focused on the mathematics underlying information and coding theory. Key topics about coding theory include: linear codes, Hamming distance, nearest neighbor decoding, and bounds on codes. The main topic on information theory is entropy, in which we measure the uncertainty of a random variable. Other possible topics include: Huffman encoding and Kraft’s theorem, codes over finite fields, BCH codes, syndrome decoding, and low density parity check codes.
Select Syllabi
Math 463: Post-quantum Cryptography
Any time two entities need to communicate securely, but haven’t been able to prearrange a secret password — think about typing a credit card number into a new website, or sending a secure message to a new friend — public key cryptography (PKC) is used. However, it’s believed that in about a decade, quantum computers will render most of
the currently-deployed PKC systems vulnerable. This course studies secure communication in an environment where an adversary has access to a quantum computer. It starts with a survey of known quantum attacks on classical PKC systems, and then moves on to a detailed study of some of the leading candidates for quantum-resistant protocols
Prerequisites:
One of MATH 360, MATH 366, MATH 466;
One of DSCI 369, MATH 369, MATH 469
MATH 470 – Euclidean and Non-Euclidean Geometry
Euclidean and non-Euclidean geometry explores geometric properties on multiple surfaces that have different behaviors, such as different curvature and being closed or not. These surfaces include the plane, the sphere, the cylinder, the cone, the projective plane, and the hyperbolic plane. We prove foundational results common to all these examples as well as address the question of how to determine when two surfaces are different. Using these surfaces, we explore general topics within geometry, such as straight lines/geodesics, triangles and their properties (sum of the angles, Pythagorean theorems), parallelism, and parallel transport. We may also cover topics such as transformations, tilings, and the classification of closed surfaces.
Select Syllabi
MATH 474 – Introduction to Differential Geometry
Differential geometry develops the theory of calculus on curved spaces. This enables us both to perform calculations and solve optimization problems within a curved space to reason about the geometry of the space itself. For example, various notions of curvature allow us to quantify how much the space is curved.
This class is focused on the differential geometry of surfaces, though because curves play a very prominent role throughout, it also spends some time on the geometry of curves. The course develops key mathematical concepts including curvature, covariant differentiation, geodesics, and the relationship between curvature and topology expressed by the Gauss–Bonnet theorem, as well as skills including geometric visualization, symbolic and numerical calculation, and rigorous reasoning and communication.
