# Mathematics

### MATH - Mathematics

##### MATH-101: Fundamentals of Algebra (Credits: 4)

This course, which uses active, inquiry based learning, will help students become more comfortable with the fundamentals of algebra through the study of mathematical models and their applications in real-life situations. This course will prepare students for future mathematics classes such as MATH 144, Functions Modeling Change.

##### MATH-144: Functions Modeling Change (Credits: 4)

Mathematical models are representations that approximate real-world systems. This course introduces students to important classes of models (linear, quadratic, exponential, logarithmic, and trigonometric) that are commonly used to describe phenomena across many disciplines. Students will develop algebraic skills in the service of modeling, solving, and forecasting.

##### MATH-200: Special Topics (Credits: 1 to 4)

Prerequisite: consent of mathematics faculty. Offered on sufficient demand.

##### MATH-200A: Trekking Camino de Santiago VI (Credits: 4)

In this MTSE participants don't just study pilgrimage, they become pilgrims as they trek along the Camino de Santiago, a route that followed the Milky Way, from the French Pyrenees to Finisterre - end of the earth - on Spain and Portugal's Atlantic coast. This is a journey of body/soul/mind for students who crave adventure and want an immersive experience. As they trek along what was once a primitive trade route, participants will discuss the history of the Camino pilgrimage and how it has evolved over time. As the group skirts mountains and moves through verdant valleys, they discover how the environment has shaped the trail and how the pilgrim experience has shaped the world around it. In cities, small villages, and along the trail participants will immerse themselves in language and culture as they communicate with residents, farmers, hospitaleros, and other pilgrims. For almost 4 weeks, participants will live a simple life, carry what they need on their backs, sleep in simple quarters called albergues, and experience the Spanish countryside and the incredible food and people of Spain. The physical demands of this pilgrimage, coupled with the camraderie of students and faculty, create a transformative adventure that will define your college experience.

##### MATH-201: Calculus I (Credits: 4)

Functions, graphs and limits. Differential calculus of algebraic, trigonometric, exponential, and logarithmic functions with applications to geometry, the physical and life sciences, and economics.

##### MATH-202: Calculus II (Credits: 4)

Integral calculus of algebraic, trigonometric, exponential, and logarithmic functions with applications to geometry, the physical and life sciences, and economics. Sequences and series. Taylors theorem.

##### MATH-203: Multivariate Calculus (Credits: 4)

Vectors in n-space, differential calculus in several variables, vector fields, integration and its applications in several variables, line, surface, volume, and flux integrals. Green's, Stokes', and the divergence theorems.

##### MATH-210: Discrete Mathematics (Credits: 4)

Discrete mathematics is an "introduction to proof" course. We will learn basic proof techniques such as direct proof, proof by induction, proof by contradiction, and proof by contrapositive and apply them to "discrete" mathematical objects like sets, sequences, and graphs. We'll also study combinatorics, propositional logic, and functions and relations. We hope to help you learn to communicate mathematics effectively and to explore what happens in a discrete world.

##### MATH-300: Special Topics in Mathematics (Credits: 1 to 4)

Special courses offered when there is sufficient demand.

##### MATH-300A: Math History, Society, Culture (Credits: 2)

How does mathematics operate in society, and how did it come to be this way? Who does mathematics, and how? What is math, anyway, and who gets to decide? Discuss these questions with your friends in Math History, Society, and Culture. We'll learn about the mathematical contributions of some famous women in math history, examine the barriers they faced, and think about the ways those barriers still exist today. We'll think about the place mathematics holds in modern society, and the historical trends that have made it so. We'll investigate the phenomenon of algorithmic injustice and consider how to fight it. We'll look at demographics in math departments and graduate schools, read inspiring stories of resilience in the face of obstacles, and think about how those obstacles could be dismantled. We'll think about how we teach mathematics, who our approach serves, and who it doesn't. We'll examine how the universal human activities we call "mathematics" appear different in different human cultures, and envision what else "mathematics" could look like.

##### MATH-300BB: The Symmetries of Things (Credits: 2)

Symmetry is everywhere! Do you know that there are only 17 different ways to repeat a pattern on wallpaper? Do you know about the Platonic solids (polyhedra where each face is the same and all faces come together at the same angles)? There are only 5 of those in three dimensions, but there are 6 in four dimensions! We will use one of the most beautiful math books ever written, "The Symmetries of Things," by one of the most famous living mathematicians in the world, John H. Conway (and co-authors), to explore the math behind these incredible results and more. You'll never look at the tile on your bathroom floor the same way again.

##### MATH-300C: Calculus of Variations (Credits: 2)

Have you ever wondered why power lines hanging between poles take the shape they do? Or, what's the curve that takes you from point (a) to point (b) the fastest? The solutions to these and many other interesting physical problems are found using the calculus of variations. We'll learn about functionals, partial derivatives, and total derivatives; find shapes that optimize lots of interesting quantities; and investigate the "principle of least action" at the heart of physics.

##### MATH-300P: Numerical Methods With Python (Credits: 2)

We survey a wide array of numerical methods using Python 3 by taking a deeper dive into the Numpy and Scipy libraries of Python. Depending on time and interest, topics may include numerical integration, solving systems of linear equations, numerical solutions to differential equations including finite difference methods, least squares, Fourier transforms, polynomial approximation and interpolation, Monte Carlo simulations, and optimization. The focus will be on implementing working code using the higher-level functionality of Numpy and Scipy, as well as gaining an understanding of the theory behind these applications. Some prior programming experience is preferred in any language, not necessarily in Python. Please contact the instructor if you have questions about your level of preparedness.

##### MATH-308: Putnam Seminar (Credit: 1)

Preparation for the William Lowell Putnam Mathematical competition. May be taken twice for credit.

##### MATH-310: Probability and Statistics (Credits: 4)

Introduction to probability theory including combinatorial analysis, conditional probability, discrete and continuous random variables, expectation and variance, jointly distributed random variables, and sampling theory.

##### MATH-311: Linear Algebra II (Credits: 4)

Rigorous treatment of general vector spaces, linear transformations, eigenvalues and eigenvectors building on the material in Linear Algebra.

##### MATH-312: Abstract Algebra (Credits: 4)

Abstract algebra develops a language and system for studying mathematical objects and the algebraic relationships between them. For example, numbers and arithmetical operations are seen as special cases of more general structures called groups, rings, and fields. This is a rigorous, proof-based course. It is strongly recommended that students take one or more upper-division math courses and have junior or senior standing before registering for Abstract Algebra.

##### MATH-314: Foundations of Geometry (Credits: 4)

Modern axiomatic development of plane geometry and related systems. Includes investigation of finite geometry and hyperbolic geometry.

##### MATH-321: Advanced Calculus (Credits: 4)

Advanced Calculus begins with an axiomatic foundation for the real number system and proves theorems that form the basis of calculus. Topics include point-set topology of the real numbers, a treatment of limits for sequences and functions, continuity, and differentiability. This is a rigorous, proof-based course. It is strongly recommended that students take one or more upper-division math courses and have junior or senior standing before registering for Advanced Calculus.

##### MATH-323: Complex Analysis (Credits: 4)

Functions of one complex variable, analyticity, Cauchy-Riemann equations, derivatives and integrals of complex functions, complex series, and residue theory.

##### MATH-341: Topology (Credits: 4)

An introduction to topology. Topics include open and closed sets, continuity, compactness, quotient spaces, and product spaces. Applications of topology may include metric topology, knot theory, classification of surfaces, and the fundamental group.

##### MATH-362: Topics in Applied Mathematics (Credits: 4)

A range of applied mathematics topics building on a foundation of linear algebra, differential equations, and discrete mathematics. Possible topics include optimization, numerical analysis, algorithm analysis and design, algorithms on graphs and trees, math modeling, dynamical systems, and statistical learning theory. May be taken for credit more than once with instructor's approval.

##### MATH-363: Differential Equations (Credits: 4)

Differential equations are used to describe phenomena that involve change. This course includes solutions of first- and second-order differential equations with a focus on analytic, numerical, and qualitative analysis of systems of linear and non-linear differential equations. Other topics may include Laplace transforms, power series methods, Fourier series methods, and topics from partial differential equations. Applications may be drawn from physics, chemistry, biology, and the social sciences.

##### MATH-370: Machine Learning (Credits: 4)

Machine learning is the study of algorithms that use data to make predictions. Such algorithms are at the heart of diverse applications like pattern recognition, spam filtering, web searching, data mining, and artificial intelligence. This course deals with the theory and application of machine learning techniques, including such topics as perceptrons, hyperplane classification and regression, decision trees, support vector machines as Lagrangian duals, conjugate gradient descent, backpropagation training for artificial neural networks, and linear and quadratic optimization.

##### MATH-387: Undergraduate Teaching (Credit: 1)

For teaching assistants in lower division mathematics problem-solving courses. A maximum of two credit hours of MATH 387 may be applied toward the major or minor. Requires consent of program director. This course is repeatable for credit.

##### MATH-401: Directed Studies (Credits: 1 to 4)

A tutorial-based course used only for student- initiated proposals for intensive individual study of topics not otherwise offered in the Mathematics Program. Requires junior or senior standing and consent of instructor and school dean. This course is repeatable for credit.

##### MATH-440: Internship (Credits: 1 to 8)

Offers students the opportunity to integrate classroom knowledge with practical experience. Prerequisites: junior or senior standing (for transfer students, at least 15 hours completed at Westminster or permission of instructor), minimum 2.5 GPA, completion of the Career Resource Center Internship Workshop, and consent of program director and Career Center Internship Coordinator. This course is repeatable for credit. REGISTRATION NOTE: Registration for internships is initiated through the Career Center website and is finalized upon completion of required paperwork and approvals. More info: 801-832-2590 <a>https://westminstercollege.edu/internships</a>

##### MATH-485: Senior Seminar (Credits: 2)

This class will collaboratively review the core areas of undergraduate mathematics and build a more complete and integrated view of mathematics. All students will be required to take the Mathematics ETS exam at the conclusion of the course. Teaching and academic majors must register for the Senior Seminar during the spring semester of their senior year. Students who will be student teaching during that semester may take it the previous year. Prerequisites: Senior standing and graduation expected by the following December or permission of the instructor. Offered every Spring semester. (WCore: SC)