Mathematics (MATH)
MATH 101 Working with Data (1 Credit)
Techniques for analyzing data are described in ordinary English without emphasis on mathematical formulas. The course focuses on graphical and descriptive techniques for summarizing data, design of experiments, sampling, analyzing relationships, statistical models, and statistical inference. Applications are drawn from everyday life: drug testing, legal discrimination cases, and public opinion polling. Not open to students who have received credit for BIO 244, ECON 250 or 255, ENVR 181, MATH 215 or 315, PLTC 218, PSYC 218, or SOC 305.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
MATH 105 Calculus I (1 Credit)
While the word calculus originally meant any method of calculating, it has come to refer more specifically to the fundamental ideas of differentiation and integration that were first developed in the seventeenth century. The subject's early development was intimately connected with understanding rates of change within the context of the physical sciences. Since then, it has proven to be widely applicable throughout the natural sciences and some social sciences, as well as crucial to the development of most modern technology. This course develops the key notions of derivatives and integrals and their interrelationship, as well as applications. An emphasis is placed on conceptual understanding and interpretation, as well as on computational skills. Students concurrently enroll in a discussion section. Students must read the <a href="http://www.bates.edu/mathematics/academics/selecting-first-math-course/">mathematics department calculus questions page </a>before registering. Not open to students who have Calculus on their high school transcripts with a grade of B or above, or who have received equivalent course credit through AP, IB, or A-Level examination scores. Successful completion of MATH 106 or 206 fulfills all Bates requirements for MATH 105. Not open to students who have received credit for MATH 206.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
Instructor: Laura Storch
MATH 106 Calculus II (1 Credit)
A continuation of Calculus I. Further techniques of integration, both symbolic and numerical, are studied. The course then treats applications of integration to problems drawn from fields such as physics, biology, chemistry, economics, and probability. Differential equations and their applications are also introduced, as well as approximation techniques and Taylor series. Students concurrently enroll in a discussion section. Recommended background: MATH 105 or equivalent. Students must read the mathematics department calculus questions page before registering. Not open to students who have received equivalent course credit through AP, IB, or A-Level examination scores. Successful completion of MATH 106 fulfills all Bates requirements for MATH 105. Successful completion of MATH 206 fulfills all Bates requirements for MATH 106. Not open to students who have received credit for MATH 206.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
MATH 110 Great Ideas in Mathematics (1 Credit)
Is mathematics composed of impenetrable formulas to be memorized, a series of insurmountable cliffs to be scaled? Are there individuals who can think logically and creatively, but never "do math"? In this course, students are asked to use their imagination to grapple with challenging mathematical concepts. The process enables them to master techniques of effective thinking, experience the joy of discovering new ideas, and feel the power of figuring out things on their own. Together they contemplate some of the greatest and most intriguing creations of human thought Not open to students who have received credit for ECON 250 or 255 or any math course numbered 200 or above.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
Instructor: Scott Balcomb
MATH 117 Introduction to Data Science: Data Visualization (1 Credit)
This course offers an introduction to data science through data visualization. Through hands-on assignments, students will develop their skills in data cleaning, analysis, and visualization using the R programming language and Github for version control. In the course students will learn to calculate and describe data using descriptive statistics and how to create a range of data visualizations to explore variation and covariation in data. Students will also learn to critique and reflect on data visualizations encountered in everyday life. No prior experience in data science or programming is necessary, making this course accessible to all students interested in exploring the dynamic field of data science. Not open to students who have received credit for DCS 210.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): (DCS: Data Science & Analysis)
Class Restriction: None
Cross-listed Course(s): DCS 117
Instructor: Laurie Baker
MATH 205 Linear Algebra (1 Credit)
Vectors and matrices are introduced as devices for the solution of systems of linear equations with many variables. Although these objects can be viewed simply as algebraic tools, they are better understood by applying geometric insight from two and three dimensions. This leads to an understanding of higher dimensional spaces and to the abstract concept of a vector space. Other topics include orthogonality, linear transformations, determinants, and eigenvectors. This course should be particularly useful to students majoring in any of the natural sciences or economics. Prerequisite(s): MATH 105 or 106.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
MATH 206 Multivariable Calculus (1 Credit)
This course extends the ideas of Calculus I and II to deal with functions of more than one variable. While calculations make straightforward use of the techniques of single-variable calculus, more effort must be spent in developing a conceptual framework for understanding curves and surfaces in higher-dimensional spaces. Topics include partial derivatives, derivatives of vector-valued functions, vector fields, integration over regions in the plane and three-space, and integration on curves and surfaces. Prerequisite(s): MATH 106.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
MATH 214 Probability (1 Credit)
Probability theory is the foundation on which statistical data analysis depends. This course together with its sequel, MATH 215, covers topics in mathematical statistics. Both courses are recommended for math majors with an interest in applied mathematics and for students in other disciplines, such as psychology and economics, who wish to learn about some of the mathematical theory underlying the methodology used in their fields. Prerequisite(s): MATH 206.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
MATH 215 Statistics (1 Credit)
The sequel to MATH 214. This course explores inferential methods in statistics. Topics may include sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, and linear regression. While applications are discussed, considerable emphasis is placed on the mathematical theory of statistics. Prerequisite(s): MATH 214.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
MATH 219 Differential Equations (1 Credit)
A differential equation is a relationship between a function and its derivatives. Many real-world situations can be modeled using these relationships. This course is a blend of the mathematical theory behind differential equations and their applications. The emphasis is on first- and second-order linear equations. Topics include existence and uniqueness of solutions, graphical approaches, numerical methods, and applications such as population modeling and mechanical vibrations. Prerequisite(s): MATH 205 and either 106 or 206.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
Instructor: Peter Wong
MATH 221 Introduction to Abstraction (1 Credit)
An intensive development of the important concepts and methods of abstract mathematics. Students work individually, in groups, and with the instructor to prove theorems and solve problems. Students explore such topics as proof techniques, logic, set theory, equivalence relations, functions, and algebraic structures. Writing is a main focus, with emphasis on mathematical conventions, expectations, and presentation, including the use of LaTeX for typesetting symbols and formulas. The course provides exposure to what it means to be a mathematician.
Modes of Inquiry: None
Writing Credit: [W2]
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
Instructor: Meredith Greer
MATH 225 Number Theory (1 Credit)
The theory of numbers is concerned with the properties of the integers, one of the most basic mathematical sets. Seemingly naive questions of number theory stimulated much of the development of modern mathematics and still provide rich opportunities for investigation. Topics include classical ones such as primality, congruences, quadratic reciprocity, and Diophantine equations, as well as more recent applications to cryptography. Additional topics such as computational methods, elliptic curves, or an introduction to analytic methods may be included. Prerequisite(s): MATH 205.
Modes of Inquiry: None
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
Instructor: Grace Coulombe
MATH 233 Mathematics for Social Justice (1 Credit)
This course teaches quantitative literacy, critical thinking and problem solving skills in a socially relevant context. Students use mathematics as a powerful analytic framework for understanding and developing realistic solutions to issues of social, political, and economic justice. The overarching goal of this course is for students to develop the ability and inclination to use mathematics to understand, and improve, the world around them. Prerequisite(s): MATH 106. Recommended background: MATH 205.
Modes of Inquiry: None
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
Instructor: Katherine Ott
MATH 255A Mathematical Models in Biology (1 Credit)
Mathematical models are increasingly important throughout the life sciences. This course provides an introduction to a variety of models in biology, with concrete examples chosen from biological and medical fields. Students work both theoretically and with computer software to analyze models, compute numerical results, and visualize outcomes. Prerequisite(s): MATH 205.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): GEC C006, GEC C065
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): BIO 255A
Instructor: Meredith Greer
MATH 301 Real Analysis (1 Credit)
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
Instructor: Katy Ott
MATH 303 Introduction to Algebraic Topology (1 Credit)
An introductory course in the field of Algebraic Topology. Students will be exposed to basic algebraic and topological structures, along with an introduction to homotopy theory and associated theorems. Students will also be introduced to homology and cohomology, and computational methods using simplicial complexes. Prerequisite(s): Math 205 and 221.
Modes of Inquiry: None
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
MATH 306 Advanced Linear Algebra (1 Credit)
Modes of Inquiry: None
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
MATH 308 Complex Analysis (1 Credit)
This course extends the concepts of calculus to deal with functions whose variables and values are complex numbers. Instead of producing new complications, this leads to a theory that is not only more aesthetically pleasing, but is also more powerful. The course should be valuable to those interested in pure mathematics as well as those who need additional computational tools for physics or engineering. Topics include the geometry of complex numbers, differentiation and integration, representation of functions by integrals and power series, and the calculus of residues. Prerequisite(s): MATH 205 and 206.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
MATH 309 Abstract Algebra I (1 Credit)
An introduction to basic algebraic structures common throughout mathematics. These may include the integers and their arithmetic, modular arithmetic, rings, polynomial rings, ideals, quotient rings, fields, and groups. Prerequisite(s): MATH 205, and 221.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
MATH 312 Geometry (1 Credit)
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
Instructor: Peter Wong
MATH 316 PIC Math: Community Engaged Data Science (1 Credit)
This PIC Math (Preparation for Industrial Careers in Mathematical Sciences) course is intended for students with a strong interest in industrial applications of mathematics and computation. Students work in teams on a research problem identified by a community partner from business, industry, or government. Students develop their mathematical and programming skills as well as skills and traits valued by employers of STEM professionals, such as teamwork, effective communication, independent thinking, problem solving, and final products. Prerequisite(s): MATH 205 and 206.
Modes of Inquiry: None
Writing Credit: None
GEC(s): GEC C091
Department/Program Attribute(s): (DCS: Community Engagement), (DCS: Praxis)
Class Restriction: Not open to: First Year students
Cross-listed Course(s): DCS 316
MATH 331 Mathematics for Machine Learning (1 Credit)
This course begins with linear regression models and introduces students to a variety of techniques for learning from data, as well as principled methods for assessing and comparing models. Topics include bias-variance trade-off, resampling and cross-validation, linear model selection and regularization, classification and regression trees, bagging, boosting, random forests, support vector machines, generalized additive models, principal component analysis, unsupervised learning and k-means clustering. Emphasis is placed on the mathematics behind these concepts and on the statistical computing in a high-level language (e.g. R or Python). Recommended background: prior coursework in programming and statistics. Prerequisite(s): MATH 205.
Modes of Inquiry: [QF], [SR]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): DCS 331
Instructor: Fatou Sanogo
MATH 355A Numerical Analysis (1 Credit)
This course studies the best ways to perform calculations that have already been developed in other mathematics courses. For instance, if a computer is to be used to approximate the value of an integral, one must understand both how quickly an algorithm can produce a result and how trustworthy that result is. While students implement algorithms on computers, the focus of the course is the mathematics behind the algorithms. Topics may include interpolation techniques, approximation of functions, solving equations, differentiation and integration, solution of differential equations, iterative solutions of linear systems, and eigenvalues and eigenvectors. Prerequisite(s): MATH 106 and 205.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): (DCS: Programming & Theory)
Class Restriction: Not open to: First Year students
Cross-listed Course(s): DCS 355A
Instructor: Laura Storch
MATH 355D Chaotic Dynamical Systems (1 Credit)
The field of dynamical systems is best understood from both theoretical and computational viewpoints, as each informs the other. Students explore attracting and repelling cycles and witness the complicated dynamics and chaos a simple function can exhibit. Topics include chaos in discrete versus continuous dynamical systems, bifurcations, and attractors, with applications to biology and physics. While there will be a significant computational component to the course, previous coding experience is not required. Recommended background: MATH219. Prerequisite(s): MATH205.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): (DCS: Programming & Theory)
Class Restriction: Not open to: First Year students
Cross-listed Course(s): DCS 355D
Instructor: Laura Storch
MATH 355H Numerical Linear Algebra (1 Credit)
This course studies the best ways to perform calculations that have been developed in Linear Algebra. Topics may include solving systems of equations, error and condition numbers, least squares, and eigenvalues and singular values. Prerequisite(s): MATH 205.
Modes of Inquiry: None
Writing Credit: None
GEC(s): GEC C006
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): DCS 355H
MATH 360 Independent Study (1 Credit)
Students, in consultation with a faculty advisor, individually design and plan a course of study or research not offered in the curriculum. Course work includes a reflective component, evaluation, and completion of an agreed-upon product. Sponsorship by a faculty member in the program/department, a course prospectus, and permission of the chair are required. Students may register for no more than one independent study per semester. This course may not be used to fulfill requirements for the mathematics major or minor in mathematics.
Modes of Inquiry: None
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
MATH 457 Senior Thesis (1 Credit)
Modes of Inquiry: None
Writing Credit: [W3]
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year, Sophomore, or Junior students
Cross-listed Course(s): None
MATH 458 Senior Thesis (1 Credit)
Modes of Inquiry: None
Writing Credit: [W3]
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year, Sophomore, or Junior students
Cross-listed Course(s): None
MATH 495B Generalized Stokes Theorem (1 Credit)
The famous theorems of Gauss, Green, and Stokes in multivariable calculus have many important applications in the study of electromagnetic fields, heat diffusion, fluid dynamics, and complex analysis. Moreover, they are all generalizations of the (one dimensional) Fundamental Theorem of Calculus. These results assert that a certain (k dimensional) integral over a region is the (k-1 dimensional) integral over the boundary of the region, culminating in the so-called Generalized Stokes Theorem. This seminar aims to explore this general form of the classical Stokes Theorem and related topics, including the concept of differential forms. Prerequisite(s): MATH 301 or 309.
Modes of Inquiry: [QF], [SR]
Writing Credit: [W3]
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year, Sophomore, or Junior students
Cross-listed Course(s): None
Instructor: Peter Wong
MATH 495F Mathematical Exposition (1 Credit)
Students in this course will explore mathematical concepts through primary sources and then prepare expository pieces aimed at varying audiences. They will also review math writing in the popular press. Students consider advanced topics in fields related to the instructors' expertise.
Modes of Inquiry: None
Writing Credit: [W3]
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year, Sophomore, or Junior students
Cross-listed Course(s): None
Instructor: Katherine Ott
MATH 495N Writing Mathematics with Data (1 Credit)
The ultimate goal of this course is for students to produce data-driven mathematical articles that are ready for publication in a variety of venues that value both content and exposition. From the start, the class reads and analyzes articles from several such venues, identifying the features that are common in many of the most enjoyable articles. Mathematical topics of focus will be applications, involving data, of ideas from Bates courses including Linear Algebra, Multivariable Calculus, and more. We derive additional motivation and context through discussions of metacognition, models of scholarship, and frameworks of learning. In all, this senior seminar serves as a culmination of the math major by means of synthesizing ideas, creating a new scholarly product, and communicating results to an audience beyond our classroom. Prerequisite(s): MATH 221.
Modes of Inquiry: None
Writing Credit: [W3]
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year, Sophomore, or Junior students
Cross-listed Course(s): None
Instructor: Meredith Greer
MATH 495O Introduction to Computational Topology (1 Credit)
Students will explore various types of data using topological data analysis (TDA). TDA allows us to quantify certain features of data that are preserved under deformation such as stretching and folding. The course will have a heavy computational component, where students will work collaboratively to build codes that analyze their data using freely available software packages. Students will present their work to the class and write technical reports aimed at a general scientific audience. We will spend time at the beginning of the semester familiarizing ourselves with foundational topics in algebraic topology such as cubical and simplicial homology, which will provide us with the necessary background information to use the computational topology software with thoughtful understanding of the inputs and outputs. The purpose of this seminar is to familiarize students with a rapidly developing and expanding field of applied mathematics. Coding experience is recommended but not required.
Modes of Inquiry: None
Writing Credit: [W3]
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year, Sophomore, or Junior students
Cross-listed Course(s): None
Instructor: Laura Storch
MATH S35 The Mathematics of the Mad Veterinarian (0.5 Credits)
This course combines ideas from linear algebra, graph theory, basic group theory, and modern mathematical developments to explore recreational puzzles called "Mad Veterinarian" scenarios. Students use mathematics and computational tools to understand and develop solutions to these scenarios. The goal of this course is for students to engage with certain technical details in mathematics, with an eye towards whimsy and having fun. Prerequisite(s): MATH 205.
Modes of Inquiry: None
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
Instructor: Martin Montgomery
MATH S45R Introduction to Geometric Group Theory (0.5 Credits)
In the 1980s, M. Gromov introduced a new approach to the study of infinite groups, namely the study of groups as geometric objects. Since then, the field of geometric group theory has flourished and is one of the most active areas of current mathematical research. This course presents the rudiments of geometric group theory. Recommended background: MATH 309. Prerequisite(s): MATH 221.
Modes of Inquiry: [QF]
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: Not open to: First Year students
Cross-listed Course(s): None
Instructor: Peter Wong
MATH S45T Mathematical Image Processing (0.5 Credits)
This course introduces mathematical methods in digital image processing, including basic image processing tools and techniques with an emphasis on their mathematical foundations. Students implement the theory using MATLAB. Topics may include image filtering, image enhancement, edge detection, and image segmentation. Prerequisite(s): MATH 205 or 206.
Modes of Inquiry: None
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): (DCS: Programming & Theory)
Class Restriction: None
Cross-listed Course(s): DCS S45T
Instructor: Katy Ott
MATH S45U A Crash Course in Galois Theory (0.5 Credits)
This course is an introduction to Galois theory, concentrating on what Galois worked on - what we today call "number fields." Number fields are the rational numbers and simple extensions of them. In this setting, students will explore the deep connections between fields and groups, culminating in the Fundamental Theorem of Galois Theory. Students will also explore some of the consequences of Galois theory, such as the impossibility of squaring the circle. Prerequisite(s): MATH 221, and MATH 225 or 309.
Modes of Inquiry: None
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None
MATH S50 Independent Study (0.5 Credits)
Students, in consultation with a faculty advisor, individually design and plan a course of study or research not offered in the curriculum. Course work includes a reflective component, evaluation, and completion of an agreed-upon product. Sponsorship by a faculty member in the program/department, a course prospectus, and permission of the chair are required. Students may register for no more than one independent study during a Short Term. May not be used to fulfill the requirement for the mathematics major or concentration in mathematics.
Modes of Inquiry: None
Writing Credit: None
GEC(s): None
Department/Program Attribute(s): None
Class Restriction: None
Cross-listed Course(s): None