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

## 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

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## MATH 151 – Mathematical Algorithms in Matlab

## MATH 155 – Calculus for Biological Scientists

## 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

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## MATH 229 – Matrices & Linear Equations

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## MATH 230 – Discrete Mathematics for Educators

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## MATH 235 – Introduction to Mathematical Reasoning

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## MATH 255 – Calculus for Biological Scientists II

## MATH 256 – Mathematics for Computational Science II

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## MATH 261 – Calculus III

Course Description: 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.

## MATH 271 – Applied Mathematics for Chemists I

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## MATH 272 – Applied Mathematics for Chemists II

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## 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

## MATH 331 – Introduction to Mathematical Modeling

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## MATH 340 – Intro to Ordinary Differential Equations

## 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 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

## MATH 384 – Supervised College Teaching

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## 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.

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## MATH 417 – Advanced Calculus I

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## 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.

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## 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.

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## MATH 435 – Projects in Applied Mathematics

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## MATH 450 – Introduction to Numerical Analysis I

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## 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.

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## 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.

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## MATH 470 – Euclidean and Non-Euclidean Geometry

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## 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 prominant 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.