Mathematical Sciences
Mathematics is one of the oldest disciplines of study. For all its antiquity, however, it is a modern, rapidly growing field. Only 70 years ago, mathematics might have been said to consist of algebra, analysis, number theory and geometry. Today, so many new areas have sprouted that the term “mathematics” seems almost inadequate. A new phrase, “the mathematical sciences” has come into fashion to describe a broad discipline that includes the blossoming fields of statistics, operations research, biomathematics and information science, as well as the traditional branches of pure and applied mathematics.
Department Update
Requirements & Courses
Goals for Majors in Mathematics
 Given a problem, to recognize its mathematical aspects and to produce an abstract mathematical model for the problem.
 Basic mathematical skills (through discrete math, the calculus course, and linear algebra).
 To write mathematics effectively.
 To understand and write mathematical proofs.
 To speak mathematics or statistical terms effectively in oral presentations.
 To use technology appropriately to learn and understand mathematics.
Goals for Majors in MST
 Solid preparation for success in graduate school in statistics, biostatistics or other quantitative fields.
 Given a problem, be able to recognize its mathematical aspects and produce an abstract mathematical model for the problem.
 Mastery of foundational mathematical skills (through discrete math, the calculus courses, linear algebra and analysis), including the ability to read and write proofs.
 Fit and interpret statistical models, including but not limited to linear regression models. Use models to make predictions and evaluate the efficacy of those models and the accuracy of those predictions.
 Understand the strengths and limitations of different research methods for the collection, analysis and interpretation of data. Be able to design studies for various purposes.
 Attend to and explain the role of uncertainty in inferential statistical procedures.
 Write a professionallevel statistical report.
 Understand the mathematical foundations of statistical inference.
 Compute with data in at least one highlevel programming language, as evidenced by the ability to analyze a complex data set.
Mathematics Major
Requirements
The mathematics major has a foundation requirement, a core requirement, a depth requirement and a total credit requirement.
 Foundation: MTH 111, MTH 112, MTH 153, MTH 211 and MTH 212
 Core
 One course in algebra: MTH 233 or MTH 238
 One course in analysis MTH 280 or MTH 281
 Depth: One advanced course, (a MTH course with a course number between 310 and 390)
 Electives to reach 36 credits at or above MTH 153
 With the approval of the department, up to 8 of the credits may be satisfied by courses taken outside the department of Mathematical Sciences. Courses taken outside the department must contain either substantial mathematical content at a level more advanced than MTH 211 and MTH 212 or statistical content at a level more advanced than SDS 220. Generally, such a 4credit course will be given 2 credits toward the mathematics major.
 Crosslisted courses (see the Courses tab) are counted as mathematics courses and given full credit toward the mathematics major, as does ECO 220.
 The following courses meet the criteria for 2 credits toward mathematics major: AST 337, CHM 331, CHM 332, CSC 240, CSC 252, CSC 274, a topic in CSC 334 , ECO 240, ECO 255, EGR 220, EGR 315, EGR 320, EGR 326, EGR 374, EGR 389, PHI 102, PHY 210, PHY 317, PHY 318, PHY 319, PHY 327, and SDS 293. A student may petition the department if they wish credit for any course not on this list.
Mathematical Statistics Major
The major in mathematical statistics (MST) is designed to prepare students for graduate study in statistics and closelyrelated disciplines (e.g., biostatistics). The mathematical statistics major overlaps with the major in statistical & data sciences (SDS), but places a heavier emphasis on the theoretical development of statistics. Mathematical statistics majors will develop sophisticated mathematical skills to prepare for rigorous future study. The major also overlaps with the major in mathematical sciences (MTH), but focuses on statistics and replaces the algebra requirement with a computing requirement.
A student majoring in MST cannot have a second major in either SDS or MTH. Students contemplating a double major in MTH and SDS should choose to major in MST.
Requirements
Ten courses
 Mathematical foundations (3 courses): MTH 153, MTH 211 and MTH 212
 Statistical foundations (2 courses)
 SDS 201 or SDS 220
 SDS 291
 Statistics depth (1 course): SDS 290, SDS 293/ CSC 293 or a topic in SDS 390
 Mathematics depth (1 course): MTH 280 or MTH 281
 Programming (1 course): SDS 192, CSC 110 or CSC 120
 Theoretical statistics (2 courses): MTH 246 and MTH 320/ SDS 320
 Electives to complete ten courses. Five College course in statistics, mathematics and computer science may be taken as electives. Students should consult with their adviser to determine appropriate electives.
Major Requirement Details
 SDS 220 or SDS 201 may be replaced by a 4 or 5 on the AP statistics exam. Replacement by AP scores does not diminish the total of 10 courses required for the major (see Electives above).
 A student may replace MTH 153, MTH 211 and MTH 212 with equivalent courses as approved by the MTH department.
 Any one of ECO 220, GOV 203, PSY 201 or SOC 204 may directly substitute for SDS 220 or SDS 201 without the need to take another course. Note that SDS 220 and ECO 220 require Calculus.
 Normally, all courses that are counted towards either the major or minor must be taken for a letter grade.
Honors
A student majoring in mathematics may apply for the departmental honors program. An honors project consists of directed reading, investigation and a thesis. This is an opportunity to engage in scholarship at a high level. A student at any level considering an honors project is encouraged to consult with the director of honors and any member of the department to obtain advice and further information.
Normally, a student who applies to do honors work must have an overall 3.0 GPA for courses through their junior year, and a 3.3 GPA for courses in their major. A student may apply either in the second semester of their junior year or by the second week of the first semester of their senior year; the former is strongly recommended.
Requirements
 Credits required for the major
 MTH 430D or MTH 432D (for either eight or twelve credits) or (in unusual circumstances) MTH 431. The length of the thesis depends upon the topic and the nature of the investigation and is determined by the student, their adviser and the department.
 An oral presentation of the thesis
The department recommends the designation of Highest Honors, High Honors, Honors, Pass or Fail based on the following three criteria at the given percentages:
60 percent thesis
20 percent oral presentation
20 percent grades in the major
Specific guidelines and deadlines for completion of the various stages of an honors project are set by the department as well as by the college. The student should obtain the department’s requirements and deadlines from the director of honors.
Mathematics Minor
Requirements
Twenty credits
 MTH 211
 Two courses (minimum of 8 credits) from MTH 153, MTH 205/ CSC 205 or courses above MTH 211.
 Two courses (minimum of 8 credits) above MTH 212.
Up to four credits may be replaced by eight credits from the list of courses outside the department in the description of major requirements found on the Major tab.
Applied Statistics Minor
Information on the interdepartmental minor in applied statistics can be found on the Statistical and Data Sciences page of this catalog.
Course Information
A student with three or four years of high school mathematics (the final year may be called precalculus, trigonometry, functions, or analysis), but no calculus, normally enrolls in MTH 111. A student with a year of AB calculus, A levels or IB math SL normally enrolls in MTH 153 and/or MTH 112 during the first year. Placement in MTH 112 is determined not only by the amount of previous calculus but also by the strength of the student’s preparation. If a student has a year of BC calculus or IB math HL, they may omit MTH 112.
A student with two years of high school mathematics, but no calculus or precalculus, should enroll in MTH 102.
Topics offered in MTH 105 are intended for students not expecting to major in mathematics or the sciences.
A student who receives credit for taking MTH 111 may not have AP calculus credits applied toward their degree. A student with 8 AP Calculus credits (available to students with a 4 or 5 on the AP exam for BC Calculus) may apply only 4 of them if they also receive credit for MTH 112. A student who has a score of 4 or 5 on the AP Statistics examination may receive 4 credits. They may not however, use them toward their degree requirements if they also receive credit for SDS 201, SDS 220, PSY 201 or ECO 220. (AP credits can be used to meet degree requirements only under circumstances specified by the college.)
Courses
MTH 101/ IDP 101 Math Skills Studio (4 Credits)
Offered as MTH 101 and IDP 101. This course is for students who need additional preparation to succeed in courses containing quantitative material. It provides a supportive environment for learning or reviewing, as well as applying, arithmetic, algebra and mathematical skills. Students develop their numerical and algebraic skills by working with numbers drawn from a variety of sources. This course does not carry a Latin Honors designation. Enrollment limited to 20. Instructor permission required.
Fall, Interterm
MTH 102 Elementary Functions (4 Credits)
Linear, polynomial, exponential, logarithmic and trigonometric functions graphs, verbal descriptions, tables and mathematical formulae. For students who intend to take calculus or quantitative courses in scientific fields, economics, government and sociology. Also recommended for prospective teachers preparing for certification. Enrollment limited to 25. {M}
Fall
MTH 103/ IDP 103 Precalculus and Calculus Bootcamp (2 Credits)
Offered as IDP 103 and MTH 103. This course provides a fastpaced review of and intense practice of computational skills, graphing skills, algebra, trigonometry, elementary functions (precalculus) and computations used in calculus. Featuring a daily review followed by problemsolving drills and exercises stressing technique and application, this course provides concentrated practice in the skills needed to succeed in courses that apply elementary functions and calculus. Students gain credit by completing all course assignments. This course does not count towards the Mathematics or Mathematical Statistics majors. S/U only. Enrollment limited to 20. Instructor permission required.
Fall, Interterm, Spring, Variable
MTH 104/ CHM 104 We Are All Scientists: The Impact of Racism on Science (4 Credits)
Offered as CHM 104 and MTH 104. "Do I belong here?" is the question that underrepresented individuals in STEM constantly ask themselves, especially at the undergraduate level where students select majors that often define their careers. The definition and specialization of science emerged in later centuries and were defined by European standards in a way that excluded the underrepresented groups that the science community struggles to include today. The interpretation of history is firmly linked to how one perceives themself. This course aims to reexamine scientific discovery with a focus on antiblackness using inclusive historical examples. We are all scientists, and it’s time to celebrate all of our stories. Enrollment limited to 15. Instructor permission required. (E)
Spring, Alternate Years
MTH 105ar Topics in Discovering MathematicsMathStudio: Making, Art + Math (4 Credits)
The course has geometrical, mathematical and studio art components. Students draw and build 3D objects with simple tools and study their geometric and mathematical properties. Introduction to elements of geometry, algebra and symmetry in connection to what is built. Enrollment limited to 25. {M}
Fall, Spring, Variable
MTH 105we Topics in Discovering MathematicsThe Mathematics of Wealth (4 Credits)
This course looks at the intersection of mathematics and social justice thru the lens of wealth in America. Social justice topics include wealth distribution, taxes, the Gini index and the poverty cycle. Mathematical topics include mathematical modeling, logic, set theory, statistics and probability. Enrollment limited to 25. (E)
Fall, Spring, Variable
MTH 111 Calculus I (4 Credits)
Discussions include rates of change, differentiation, applications of derivatives including differential equations and the fundamental theorem of calculus. Written communication and applications to other sciences and social sciences motivate course content. Enrollment limited to 25. {M}
Fall, Spring
MTH 112 Calculus II (4 Credits)
Techniques of integration, geometric applications of the integral, differential equations and modeling, infinite series, and approximation of functions. Written communication and applications to other sciences and social sciences motivate course content. Prerequisite: MTH 111 or equivalent. Enrollment limited to 25. {M}
Fall, Spring
MTH 153 Introduction to Discrete Mathematics (4 Credits)
An introduction to discrete (finite) mathematics with emphasis on the study of algorithms and on applications to mathematical modeling and computer science. Topics include sets, logic, graph theory, induction, recursion, counting and combinatorics. Enrollment limited to 25. {M}
Fall, Spring
MTH 205/ CSC 205 Modeling in the Sciences (4 Credits)
Offered as CSC 205 and MTH 205. This course integrates the use of mathematics and computers for modeling various phenomena drawn from the natural and social sciences. Scientific case studies span a wide range of systems at all scales, with special emphasis on the life sciences. Mathematical tools include data analysis, discrete and continuous dynamical systems, and discrete geometry. This is a projectbased course and provides elementary training in programming using Mathematica. Designations: Theory, Programming. Prerequisites: MTH 112. CSC 110 recommended. Enrollment limited to 20. {M}
Fall, Spring, Annually
MTH 211 Linear Algebra (4 Credits)
Systems of linear equations, matrices, linear transformations and vector spaces. Applications to be selected from differential equations, foundations of physics, geometry and other topics. Prerequisite: MTH 112 or equivalent, or MTH 111 and MTH 153; MTH 153 is suggested. Enrollment limited to 30. {M}
Fall, Spring
MTH 212 Multivariable Calculus (4 Credits)
Theory and applications of limits, derivatives and integrals of functions of one, two and three variables. Curves in twoand threedimensional space, vector functions, double and triple integrals, polar, cylindrical and spherical coordinates. Path integration and Green’s Theorem. Prerequisites: MTH 112. MTH 211 suggested (may be concurrent). Enrollment limited to 30. {M}
Fall, Spring
MTH 233 An Introduction to Abstract Algebra (4 Credits)
An introduction to the concepts of abstract algebra, including groups, quotient groups and, if time allows, rings and fields. Prerequisites: MTH 153 and MTH 211 or equivalent. {M}
Spring
MTH 238 Number Theory (4 Credits)
Topics to be covered include properties of the integers, prime numbers, congruences, various Diophantine problems, arithmetical functions and cryptography. Prerequisite: MTH 153 and MTH 211, or equivalent. {M}
Fall
MTH 246 Probability (4 Credits)
An introduction to probability, including combinatorial probability, random variables, discrete and continuous distributions. Prerequisites: MTH 153 and MTH 212 (may be taken concurrently), or equivalent. {M}
Fall
MTH 254 Combinatorics (4 Credits)
Enumeration, including recurrence relations and generating functions. Special attention paid to binomial coefficients, Fibonacci numbers, Catalan numbers and Stirling numbers. Combinatorial designs, including Latin squares, finite projective planes, Hadamard matrices and block designs. Necessary conditions and constructions. Error correcting codes. Applications. Prerequisites: MTH 153 and MTH 211 or equivalent. {M}
Spring, Alternate Years
MTH 255 Graph Theory (4 Credits)
The course begins with the basic structure of graphs including connectivity, paths, cycles and planarity and proceeds to independence, stability, matchings and colorings. Directed graphs and networks are considered. In particular, some optimization problems including maximum flow are covered. The material includes theory and mathematical proofs as well as algorithms and applications. Prerequisites: MTH 153 and MTH 211 or equivalent. {M}
Spring, Alternate Years
MTH 261 Computational Linear Algebra (4 Credits)
Linear algebra has become one of the most widely applied areas of mathematics. Fast matrix computation allows for the manipulation and analysis of large complex data sets which has enabled major advances in computation. Discussions include solving linear systems, matrices, determinants, matrix factorizations such as LU, and QR decompositions and singular value decomposition (SVD). Students will learn to use software to analyze large data sets, with applications in computer science, chemistry, engineering, and others. This course will be taught using the software MATLAB, but no knowledge of MATLAB is assumed. Enrollment limited to 25. (E) {M}
Fall, Spring, Variable
MTH 264de Topics in Applied MathDifferential Equations (4 Credits)
This course gives an introduction to the theory and applications of ordinary differential equations. The course explores different applications in physics, chemistry, biology, engineering and social sciences. Students learn to predict the behavior of a particular system described by differential equations by finding exact solutions, making numerical approximations, and performing qualitative and geometric analysis. Specific topics include solutions to first order equations and linear systems, existence and uniqueness of solutions, nonlinear systems and linear stability analysis, forcing and resonance, Laplace transforms. Prerequisites: MTH 112, MTH 212 and MTH 211 (recommended) or PHY 210, or equivalent. {M}
Fall, Spring
MTH 270ss Topics in GeometryThe Shape of Space (4 Credits)
This is a course in intuitive geometry and topology, with an emphasis on handson exploration and developing the visual imagination. Discussions may include knots, geometry and topology of surfaces and the GaussBonnet Theorem, symmetries, wallpaper patterns in Euclidean, spherical and hyperbolic geometries, and an introduction to 3dimensional manifolds. Prerequisites: MTH 211 and MTH 212 or equivalent. {M}
Fall, Spring, Variable
MTH 280 Advanced Calculus (4 Credits)
Functions of several variables, vector fields, divergence and curl, critical point theory, transformations and their Jacobians, implicit functions, manifolds, theory and applications of multiple integration, and the theorems of Green, Gauss and Stokes. Prerequisites: MTH 211 and MTH 212, or equivalent. MTH 153 is encouraged. {M}
Spring
MTH 281 Introduction to Analysis (4 Credits)
The topological structure of the real line, compactness, connectedness, functions, continuity, uniform continuity, differentiability, sequences and series of functions, uniform convergence, introduction to Lebesgue measure and integration. Prerequisites: MTH 211 and MTH 212, or equivalent. MTH 153 is strongly encouraged. Enrollment limited to 20. {M}
Fall
MTH 300 Dialogues in Mathematics and Statistics (1 Credit)
In this class students don’t do math as much as they talk about doing math and the culture of mathematics. The class includes lectures by students, faculty and visitors on a wide variety of topics, and opportunities to talk with mathematicians about their lives. This course is especially helpful for those considering graduate school in the mathematical sciences. Prerequisites: MTH 211, MTH 212 and two additional mathematics courses at the 200level, or equivalent. May be repeated once for credit. S/U only. {M}
Fall, Spring
MTH 301rs Topics in Advanced MathematicsResearch (3 Credits)
In this course students work in small groups on original research projects. Students are expected to attend a brief presentation of projects at the start of the semester. Recent topics include interactions between algebra and graph theory, plant patterns, knot theory and mathematical modeling. This course is open to all students interested in gaining research experience in mathematics. Prerequisites vary depending on the project, but normally MTH 153 and MTH 211 are required. Restrictions: MTH 301rs may be repeated once. {M}
Fall, Spring, Variable
MTH 320/ SDS 320 Mathematical Statistics (4 Credits)
Offered as MTH 320 and SDS 320. An introduction to the mathematical theory of statistics and to the application of that theory to the real world. Discussions include functions of random variables, estimation, likelihood and Bayesian methods, hypothesis testing and linear models. Prerequisites: a course in introductory statistics, MTH 212 and MTH 246, or equivalent. Enrollment limited to 20. {M}
Spring
MTH 333ct Topics in Abstract AlgebraCoding Theory (4 Credits)
An overview of noiseless and noisy coding. Covers both theory and applications of coding theory. Topics include linear codes, Hamming codes, ReedMuller codes, cyclic redundancy checks, entropy, and other topics as time permits. Prerequisites: MTH 153 and MTH 211. One of MTH 233 or MTH 238 is highly recommended. {M}
Fall, Spring, Variable
MTH 333la Topics in Abstract AlgebraAdvanced Linear Algebra (4 Credits)
This is a second course in linear algebra that explores the structure of matrices. Topics may include characteristic and minimal polynomials, diagonalization and canonical forms of matrices, the spectral theorem, the singular value decomposition theorem, an introduction to modules, and applications to problems in optimization, Markov chains, and others. {M}
Fall, Spring, Variable
MTH 333rt Topics in Abstract AlgebraRepresentation Theory (4 Credits)
Representation theory is used everywhere, from number theory, combinatorics, and topology, to chemistry, physics, coding theory, and computer graphics. The core question of representation theory is: what are the fundamentally different ways to describe symmetries as groups of matrices acting on an underlying vector space? This course will explain each part of that question and key approaches to answering it. Topics may include irreducible representations, Schur’s Lemma, Maschke’s Theorem, character tables, orthogonality of characters, and representations of specific finite groups. MTH 233 is helpful but not required. Prerequisite: MTH 211. {M}
Fall, Spring, Variable
MTH 353ac Seminar: Advanced Topics in Discrete Applied MathematicsCalderwood Seminar on Applied Algebraic Combinatorics and Mathematical Biology (4 Credits)
Calderwood Seminar. Combinatorial ideas permeate biology at all scales, from the combinatorial properties of the sequences of letters (nucleotides) representing DNA and RNA, to the symmetries often observed in cell divisions, to the graphs that can be used to represent evolutionary trees. This course focuses on key combinatorial ideas that arise on multiple scales in biology, including molecular, cellular and organism, especially: counting and classification, symmetries and combinatorial graphs. The class interviews mathematicians and biologists about their current research and prepares multiple reports and presentations for different kinds of popular audiences (for example: kids, biologists and newspapers). No particular biological background is expected. MTH 153 and an additional proofbased course are required, or equivalent. MTH 233 and MTH 254 or their equivalents are useful but not required. Restrictions: Juniors and seniors only. Enrollment limited to 12. Instructor permission required. {M}
Fall, Spring, Variable
MTH 354 Mathematics of Deep Learning (4 Credits)
The developments of Artificial Intelligence (AI) are tied to an unprecedented reshaping of the human experience throughout society, impacting the arts, literature, science, politics, commerce, law, education, etc. Despite these consequential effects, understanding of AI is mostly empirical. The state of knowledge of deep learning has been recently likened to a pseudoscience like alchemy. Progress in this direction rests on truly interdisciplinary approaches that are equally informed from mathematics, computer science, statistics and data science. The course goals are: (1) Understand the mathematical foundations of deep learning, (2) Develop proficiency in using mathematical tools to analyze deep learning algorithms, (3) Apply mathematical concepts to implement realworld applications of deep learning. Not recommended for firstyears. Prerequisites: MTH 211 and MTH 212. Enrollment limited to 12. {M}
Fall, Spring, Variable
MTH 364ds Advanced Topics in Continuous Applied MathematicsDynamical Systems, Chaos and Applications (4 Credits)
An introduction to the theory of Dynamical Systems with applications. A dynamical system is a system that evolves with time under certain rules. The class looks at both continuous and discrete dynamical systems when the rules are given by differential equations or iteration of transformations. Students study the stability of equilibria or periodic orbits, bifurcations, chaos and strange attractors. Applications are often biological, but the final project is on a scientific application of the student's choice. Prerequisites: MTH 211 and MTH 212 or equivalent. {M}
Fall, Spring, Variable
MTH 364pd Advanced Topics in Continuous Applied MathematicsPartial Differential Equations (4 Credits)
Partial differential equations allow the ability to track how quantities change when they depend on multiple variables, e.g. space and time. This course provides an introduction to techniques for analyzing and solving partial differential equations and surveys applications from the sciences and engineering. Specific topics include Fourier series; separation of variables; heat, wave and Laplace’s equations; finite difference numerical methods; and introduction to pattern formations. Prerequisite: MTH 211 and MTH 212, or MTH 280/MTH 281, or equivalent. MTH 264 is strongly recommended. Prior exposure to computing (using Matlab, Mathematica, Python, etc.) is helpful. {M}
Fall, Spring, Variable
MTH 370gw Topics in Topology and GeometryThe Geometry of the Physical World (4 Credits)
The course covers the mathematics needed to describe our physical universe, focusing on concepts from the field of Differential Geometry that are needed to understand the Theories of Special and General Relativity. The course cover the differential geometry of surfaces in 3dimensional space, with a particular focus on the difference between intrinsic and extrinsic geometry. The course also covers the Postulates of Special Relativity and an introduction to General Relativity, motivating the study of higher dimensional manifolds, Lorentzian Geometry and the mathematics behind coordinateindependent Physical theories. (E) {M}{N}
Fall, Spring, Variable
MTH 370tp Topics in Topology and GeometryTopology (4 Credits)
Topology is a kind of geometry in which important properties of a shape are preserved under continuous motions (homeomorphisms)—for instance, properties like whether one object can be transformed into another by stretching and squishing but not tearing. This course gives students an introduction to some of the classical topics in the area: the basic notions of point set topology (including connectedness and compactness) and the definition and use of the fundamental group. Prerequisites: MTH 280 or MTH 281, or equivalent. {M}
Fall, Spring, Variable
MTH 381fw Topics in Mathematical Analysis Fourier Analysis and Wavelets (4 Credits)
The mathematics of how it is possible to simultaneously stream videos while using the same cable to call on the phone. Hilbert spaces, Fourier series, Fourier transform, discrete Fourier transforms, wavelets, multiresolution analysis, applications. Prerequisite: MTH 280 or MTH 281. {M}
Fall, Spring, Variable
MTH 381gm Topics in Mathematical AnalysisGeometry and Mechanics (4 Credits)
Introduction to modern geometric approaches to classical physics. The essential idea is that the notion of symmetry can be used to simplify the analysis of physical systems. Topics may include Lagrangian and Hamiltonian mechanics, Noether’s Theorem and conservation laws, quantization, and special relativity. MTH 233 is suggested (possibly concurrently). No prior exposure to physics is necessary. Prerequisite: MTH 280 or MTH 281. {M}
Fall, Spring, Variable
MTH 382 Complex Analysis (4 Credits)
Complex numbers, functions of a complex variable, algebra and geometry of the complex plane. Differentiation, integration, Cauchy integral formula, calculus of residues, applications. Prerequisite: MTH 211 and MTH 212, or equivalent.
Fall, Spring, Variable
MTH 400 Special Studies (14 Credits)
Normally for majors who have had at least four semester courses at the intermediate level. Instructor permission required.
Fall, Spring
MTH 430D Honors Project (4 Credits)
Department permission required.
Fall, Spring
MTH 431 Honors Project (8 Credits)
Department permission required.
Fall, Spring
MTH 432D Honors Project (6 Credits)
Department permission required.
Fall, Spring
MTH 580 Graduate Special Studies (4 Credits)
Instructor permission required.
Fall, Spring
Crosslisted Courses
CHM 104/ MTH 104 We Are All Scientists: The Impact of Racism on Science (4 Credits)
Offered as CHM 104 and MTH 104. "Do I belong here?" is the question that underrepresented individuals in STEM constantly ask themselves, especially at the undergraduate level where students select majors that often define their careers. The definition and specialization of science emerged in later centuries and were defined by European standards in a way that excluded the underrepresented groups that the science community struggles to include today. The interpretation of history is firmly linked to how one perceives themself. This course aims to reexamine scientific discovery with a focus on antiblackness using inclusive historical examples. We are all scientists, and it’s time to celebrate all of our stories. Enrollment limited to 15. Instructor permission required. (E)
Spring, Alternate Years
CSC 109/ SDS 109 Communicating with Data (4 Credits)
Offered as SDS 109 and CSC 109. The world is growing increasingly reliant on collecting and analyzing information to help people make decisions. Because of this, the ability to communicate effectively about data is an important component of future job prospects across nearly all disciplines. In this course, students learn the foundations of information visualization and sharpen their skills in communicating using data. This course explores concepts in decisionmaking, human perception, color theory and storytelling as they apply to datadriven communication. This course helps students build a strong foundation in how to talk to people about data, for both aspiring data scientists and students who want to learn new ways of presenting information. Enrollment limited to 40. {M}
Fall, Spring
CSC 205/ MTH 205 Modeling in the Sciences (4 Credits)
Offered as CSC 205 and MTH 205. This course integrates the use of mathematics and computers for modeling various phenomena drawn from the natural and social sciences. Scientific case studies span a wide range of systems at all scales, with special emphasis on the life sciences. Mathematical tools include data analysis, discrete and continuous dynamical systems, and discrete geometry. This is a projectbased course and provides elementary training in programming using Mathematica. Designations: Theory, Programming. Prerequisites: MTH 112. CSC 110 recommended. Enrollment limited to 20. {M}
Fall, Spring, Annually
CSC 270 Digital Circuits and Computer Systems (5 Credits)
This class introduces the operation of logic and sequential circuits. Students explore basic logic gates (AND, OR, NAND, NOR), counters, flipflops, decoders, microprocessor systems. Students have the opportunity to design and implement digital circuits during a weekly lab. Designation: Systems. Prerequisite: CSC 231. Enrollment limited to 12.
Fall, Spring, Variable
CSC 290 Introduction to Artificial Intelligence (4 Credits)
An introduction to artificial intelligence including an introduction to artificial intelligence programming. Discussions include: game playing and search strategies, machine learning, natural language understanding, neural networks, genetic algorithms, evolutionary programming and philosophical issues. Designations: Theory, Programming. Prerequisite: CSC 210 and MTH 111, or equivalent. Enrollment limited to 30.
Fall, Spring, Variable
IDP 101/ MTH 101 Math Skills Studio (4 Credits)
Offered as MTH 101 and IDP 101. This course is for students who need additional preparation to succeed in courses containing quantitative material. It provides a supportive environment for learning or reviewing, as well as applying, arithmetic, algebra and mathematical skills. Students develop their numerical and algebraic skills by working with numbers drawn from a variety of sources. This course does not carry a Latin Honors designation. Enrollment limited to 20. Instructor permission required.
Fall, Interterm
IDP 105 Quantitative Skills in Practice (4 Credits)
A course continuing the development of quantitative skills and quantitative literacy begun in MTH/ IDP 101. Students continue to exercise and review basic mathematical skills, to reason with quantitative information, to explore the use and power of quantitative reasoning in rhetorical argument, and to cultivate the habit of mind to use quantitative skills as part of critical thinking. Attention is given to visual literacy in reading graphs, tables and other displays of quantitative information and to cultural attitudes surrounding mathematics. Prerequisites: MTH 101/ IDP 101. Enrollment limited to 18. {M}
Spring
IDP 325 Art/Math Studio (4 Credits)
This course is a combination of two distinct but related areas of study: studio art and mathematics. Students are actively engaged in the design and fabrication of threedimensional models that deal directly with aspects of mathematics. The class includes an introduction to basic building techniques with a variety of tools and media. At the same time each student pursues an intensive examination of a particularindividualtheme within studio art practice. The mathematical projects are pursued in small groups. The studio artwork is done individually. Group discussions of reading, oral presentations and critiques, as well as several small written assignments, are a major aspect of the class. Limited to juniors and seniors. Instructor permission required. Enrollment limited to 15. {A}{M}
Spring
MTH 320/ SDS 320 Mathematical Statistics (4 Credits)
Offered as MTH 320 and SDS 320. An introduction to the mathematical theory of statistics and to the application of that theory to the real world. Discussions include functions of random variables, estimation, likelihood and Bayesian methods, hypothesis testing and linear models. Prerequisites: a course in introductory statistics, MTH 212 and MTH 246, or equivalent. Enrollment limited to 20. {M}
Spring
PSY 201 Statistical Methods for Undergraduate Research (5 Credits)
An overview of the statistical methods needed for undergraduate research emphasizing methods for data collection, data description and statistical inference including an introduction to study design, confidence intervals, testing hypotheses, analysis of variance and regression analysis. Techniques for analyzing both quantitative and categorical data are discussed. Applications are emphasized, and students use R and other statistical software for data analysis. This course satisfies the basis requirement for the psychology major. Students who have taken MTH 111 or the equivalent or who have taken AP STAT should take SDS 220, which also satisfies the major requirement. Restrictions: Students do not normally earn credit for more than one course on this list: ECO 220, GOV 203, MTH 220, PSY 201, SDS 201, SDS 220 or SOC 204. Enrollment limited to 40. {M}
Fall, Spring, Variable
SDS 220 Introduction to Probability and Statistics (4 Credits)
(Formerly MTH 220/SDS 220). An applicationoriented introduction to modern statistical inference: study design, descriptive statistics, random variables, probability and sampling distributions, point and interval estimates, hypothesis tests, resampling procedures, and multiple regression. A wide variety of applications from the natural and social sciences are used. This course satisfies the basic requirement for biological science, engineering, environmental science, neuroscience, and psychology. Prerequisite: MTH 111, or equivalent; SDS 100 must be taken concurrently for students who have not completed SDS 192, SDS 201, SDS 290 or SDS 291. Restrictions: Students do not normally earn credit for more than one course on this list: ECO 220, GOV 203, MTH 220, PSY 201, SDS 201, SDS 220 or SOC 204. Enrollment limited to 40. {M}
Fall, Spring
SDS 290 Research Design and Analysis (4 Credits)
(Formerly MTH/SDS 290). A survey of statistical methods needed for scientific research, including planning data collection and data analyses that provide evidence about a research hypothesis. The course can include coverage of analyses of variance, interactions, contrasts, multiple comparisons, multiple regression, factor analysis, causal inference for observational and randomized studies and graphical methods for displaying data. Special attention is given to analysis of data from student projects such as theses and special studies. Statistical software is used for data analysis. Prerequisites: One of the following: PSY 201, SDS 201, GOV 203, ECO 220, SDS 220 or a score of 4 or 5 on the AP Statistics examination or the equivalent; concurrent registration in SDS 100 required for students who have not completed SDS 192, SDS 201, SDS 220 or SDS 291. Enrollment limited to 40. {M}
Fall, Spring
SDS 291 Multiple Regression (4 Credits)
(Formerly MTH 291/ SDS 291). Theory and applications of regression techniques: linear and nonlinear multiple regression models, residual and influence analysis, correlation, covariance analysis, indicator variables and time series analysis. This course includes methods for choosing, fitting, evaluating and comparing statistical models and analyzes data sets taken from the natural, physical and social sciences. Prerequisite: SDS 201, PSY 201, GOV 203, SDS 220, ECO 220 or equivalent or a score of 4 or 5 on the AP Statistics examination; concurrent registration in SDS 100 required for students who have not completed SDS 192, 201, 220 or 290. Enrollment limited to 40. {M}{N}
Fall, Spring
The Center for Women in Mathematics is a place for women to get intensive training at the advanced level and an opportunity to study in a community that is fun, friendly and serious about math. The students build the skills and confidence needed to continue on to graduate school. For details see the Postbaccalaureate Program Website.
Additional Programmatic Information
Advisers: Pau Atela, Benjamin Baumer, Jennifer Beichman, Patricia Cahn, Luca Capogna, Jacob Garcia, Christophe Golé, Rajan Mehta, Geremias Polanco, Candice Price, Ileana Streinu, Becca Thomases, Julianna Tymoczko, Ileana Vasu
If you'd like to declare a math major or minor, the first step is to fill out an advisor preference form here.
Postbaccalaureate Program
Sponsored by the Center for Women in Mathematics, the Postbaccalaureate Program is for women with bachelor's degrees who did not major in mathematics or whose mathematics major was light. This program is open to all women who have graduated college with some course work in mathematics above the level of calculus, and a serious interest in further pursuing mathematics. More information about the program is provided by the Center for Women in Mathematics.
Masters of Arts in Teaching
The Department of Mathematical Sciences cooperates with the Department of Education and Child Study to offer a one–year Master of Arts in Teaching (MAT) program.
During one summer and two semesters, MAT candidates take three courses in mathematics and all the course work required for secondary teacher certification in Massachusetts. The program includes a semester–long internship in a local school. Applicants for the MAT program in mathematics should have an undergraduate degree in mathematics. College graduates with a different major will be considered if their undergraduate education included a strong foundation in mathematics.
FifthYear Master of Science in Statistics
Qualified graduates of the Department of Mathematical Sciences can apply to the University of Massachusetts Amherst to earn a master's degree in statistics in a fifth year. Learn more about the program.
An honors project consists of directed reading, investigation and a thesis. This is an opportunity to engage in scholarship at a high level. A student at any level considering an honors project is encouraged to consult with the director of honors and any member of the department to obtain advice and further information.
Honors projects in the Department of Mathematical Sciences are worth 8–12 credits. Ideally, your program should be approved by the department in the spring before your senior year. (You might also consider applying for a summer research grant from Smith so you can spend the summer before your senior year in Northampton beginning the work on your project.)
Eligibility
Normally, a student who applies to do honors work must have an overall 3.0 GPA for courses through her junior year, and a 3.3 GPA for courses in her major. A student may apply either in the second semester of her junior year or by the second week of the first semester of her senior year; we strongly recommend the former.
Financial Assistance
The Tomlinson Memorial fund provides financial assistance for honors thesis projects. If you're interested in obtaining funds you must complete the application form "Financial Assistance for Departmental Honors" and submit it with your honors application. This application form can be obtained from the director of honors or the class deans office.
Timeline*
Typically, you meet with your project adviser several times a week. Usually the project focuses on one area and involves reading mathematics papers and books at an advanced level. The honors paper you write will be an assimilation and exposition of the area. Occasionally, a project will include new contributions by the student. By early spring, most of your research should be complete and you will begin writing. The paper is due in the middle of April. It is read by a panel of faculty members, and in early May you present a talk to the department on your work.
Presentation of Thesis
Smith College rules stipulate that the final draft of your thesis must be submitted to your faculty adviser (first reader) and second reader by April 15*. This final draft will be the one subject to evaluation by the first and second readers. Honors candidates give a 45minute oral presentation of their honors research for the mathematics faculty, which will be open to all interested members of the Smith College community and others by invitation.
You should expect to take questions from the audience during and after the presentation. Following the open presentation there will be an additional question period for the mathematics faculty only. This presentation will be scheduled during the last week of classes, or reading period, but no later than the last day of the preexamination study period.
Evaluation
 60% thesis
 20% oral presentation
 20% grades in the major
Your grade for the project (pass, distinction, high distinction, highest distinction) is determined by a combination of your grades on the paper, the presentation and your mathematics courses. The presentation has the least weight in your grade, but it gives us all a chance to hear about what you have done. We also invite you to give a talk to your fellow majors, though this is not part of the official process.
*Timeline is for May graduates. Consult your adviser about dates if you plan to graduate in January.
The Math department does not have a designated placement test for math and statistics courses. Descriptions of common starting courses, advice on how to decide between them and information about AP and IB credit is available on the Introductory Mathematics Courses website and on the document below.
Additional Course Information
Whatever your reasons to study math or statistics, we, or our colleagues in Statistics & Data Science, have something for you! And by the time you take a course with us, we hope that you will have enjoyed it so much that you will take another one just because it’s cool…
Why do I need math at all?
If you haven’t enjoyed your mathematics courses or have found them frustrating, the need to take more math in college for your major can be irritating. Or maybe you are delighted that you’ll be taking more math! Students have completely different experiences of mathematics courses, and here we would like to lay out some reasons that all students should be excited about taking math.
You have probably heard the refrain “Math is everywhere!” many times before, and it’s true: math IS everywhere. From computing your GPA (a weighted average) to understanding how debt works (compounding interest), math runs through most facets of our lives, and increasingly in the data driven industry. For instance, how should a large trucking company allocate its storage of empty trailor around the country to minimize the number of miles empty trailors travel? This is a difficult math problem that generates jobs and saves the environment!
In practical terms, even if you do not choose to do a math major, a number of other majors  and professions!  require math. The most common ones are:

MTH 111 Calculus I (Economics, Engineering, Physics, Statistics & Data Science, Prehealth)

MTH 112 Calculus II (Engineering, Physics)

MTH 153 Discrete Math (Computer Science)

MTH 211 Linear Algebra (Statistics & Data Science)

MTH 212 Calc III (Engineering, Physics)

SDS/MTH 220 Intro to Probability and Stats (Statistics & Data Science, Biology, Economics; recommended for Engineering and Prehealth)
What courses am I prepared to take?
A student who wishes to study mathematics may place herself according to the following guidelines.

Any student who is curious about mathematics outside of the standard fields seen in high school may consider Discovering Mathematics (MTH105). Some incarnation of the course have explored arts and math, the role of chance in our lives, and measuring social inequalities.

A student with three years of high school math (typically one year of geometry and two years of algebra) is ready for Elementary Functions (MTH102), which can prepare them to take Calculus I.

A student with four years of high school math (but little or no calculus) can take Calculus I (MTH111).

A student with a year of high school calculus is ready to take Discrete Mathematics (MTH153) or Calculus II (MTH112).

Wellprepared students might start at Smith with Linear Algebra (MTH211) or Calculus III (MTH212).
Below is a more detailed document matching your preparation with possible courses.
Mathematics, Statistics, and You
For statistics courses you are prepared to take, consult this Statistics and Data Science page.
For detailed information about the introductory calculus courses as Smith, including how they work and they help you do the things you want to do with your time at Smith, visit the Introductory Mathematics Courses at Smith website.
The introductory calculus courses (MTH111: Calculus 1 and MTH112: Calculus 2) at Smith are offered in small sections of 2028 students, taught by different professors. The sections of each introductory course are closely coordinated to maximize the resources available to students and make it easy for students to work together during the semester. Those resources include department peer tutors, quantitative skills tutors through the Spinelli Center for Quantitative Learning, and the department Calculus Training Group program, profiled in Grecourt Gate in November 2017.
For those who either do not intend to take Calculus or who have already taken enough of it, there is math besides Calculus!
MTH153: Introduction to Discrete Mathematics
Description: An introduction to discrete (finite) mathematics with emphasis on the study of algorithms and on applications to mathematical modeling and computer science. Topics include sets, logic, graph theory, induction, recursion, counting and combinatorics.
Offered: Every semester
Prerequisite: None, but MTH111 and familiarity with summation notation is recommended
Great for: Computer Science, Mathematics & Statistics, Statistics & Data Science – the study of logic and algorithms is necessary for good coding. In addition, you learn a variety of proof techniques, which are key for going deeper in mathematics as a whole.
MTH211: Linear Algebra
Description: Systems of linear equations, matrices, linear transformations, vector spaces. Applications to be selected from differential equations, foundations of physics, geometry and other topics.
Prerequisite: MTH 112 or the equivalent, or MTH 111 and MTH 153; MTH 153 is suggested
Offered: Every semester
Great for: Almost everyone, but specifically Computer Science, Mathematics & Statistics, Statistics & Data Science, Economics. Linear algebra is the workhorse subject of modern mathematics. Any work with data relies on an understanding of matrices. Linear algebra is even used to help identify exoplanets in astronomy! It turns up pretty much everywhere.
Required for: MTH and SDS majors.
MTH212: Calculus III
Description: Theory and applications of limits, derivatives and integrals of functions of one, two and three variables. Curves in two and three dimensional space, vector functions, double and triple integrals, polar, cylindrical, spherical coordinates. Path integration and Green’s Theorem.
Prerequisites: MTH 112. It is suggested that MTH 211 be taken before or concurrently with MTH 212.
Offered: Every semester
Great for: Physics, Engineering, Mathematics & Statistics, Economics. Calculus III takes everything from calculus and moves into multiple dimensions. For physics and engineering, understanding of more than one dimension is essential for modeling how objects move through our multidimensional space. In economics, you often need to optimize quantities with many different inputs (and sometimes outputs!) which Calculus III can do.
Required for: EGR and MTH majors.
MTH/SDS220: Introduction to Probability and Statistics
Description: An applicationoriented introduction to modern statistical inference: study design, descriptive statistics; random variables; probability and sampling distributions; point and interval estimates; hypothesis tests, resampling procedures and multiple regression. A wide variety of applications from the natural and social sciences are used. Classes meet for lecture/discussion and for a required laboratory that emphasizes analysis of real data.
Prerequisite: MTH 111 or the equivalent, or permission of the instructor. Lab sections limited to 20
Offered: Every semester
Great for: Everybody. Data analysis is a growing field and understanding how to work with data is useful in many fields. MTH 220 satisfies the basis requirement for biological science, engineering, environmental science, neuroscience and psychology.
Required for: BIO, EGR, ESP, NSC, PSY, SDS.
Note: Other departments offer statistics courses with different prerequisites, and for which SDS 220 may be substituted (e.g. PSY/SDS 201, ECO 220)
Consult the Smith College Course Catalog for information on the current courses available in mathematics and statistics.
There are also several courses that are available for credit from other departments, including art, psychology and more. Consult the catalog.
What classes you should take depends a great deal on what you find most interesting and on what your goals are. Discuss your options with your adviser and also talk to the instructors of particular courses that interest you.
If you are interested in the sciences:
The department offers a variety of courses to give you a solid mathematical experience. Calculus III and Linear Algebra are fundamental courses. You may also want to consider taking one or more of the following: Intro to Probability and Statistics, Differential Equations, Differential Equations and Numerical Methods, Discrete Mathematics, Advanced Topics in Continuous Applied Mathematics.
If you are interested in computer science:
Consider taking some of these: Calculus III, Linear Algebra, Modern Algebra, Discrete Mathematics. Many of our students are double–majoring in mathematics and computer science.
If you are interested in economics:
Calculus will give you a good, basic experience. You may consider other courses as well, so be sure to discuss your options with your adviser. If you are contemplating graduate school in economics, the economics department recommends you to take MTH 211, 212, 280 and 281. Taking a solid course in statistics is also a good idea (any of MTH 220, 246, 290, 291 and 320 would do). Many economics majors want to take MTH 264 as well. Double–majoring in mathematics and economics is a good choice.
If you are interested in applied mathematics:
The following courses work specifically with applications: MTH 205, 264, 353 and 364. Other courses that contain many applications and are important for anyone considering graduate school in applied mathematics are: MTH 220, 246, 254, 255, 280, 290, 291, and 320.
If you are interested in theoretical mathematics:
The following courses work with abstract structures: MTH 233, 238, 246, 254, 255, 280, 281, 333, 370, 381, and 382.
If you liked calculus:
There are many reasons for liking calculus. If you delighted in the geometry, for example, you should consider MTH 270, 280, 370 and 382. If you enjoyed the power of calculus to describe and understand the world, you will want to take MTH 264. If you are fascinated with the ideas of limit and infinity and want to get to the bottom of them, you should take MTH 281.
If you liked linear algebra:
You will like MTH 233 very much, and you will also like MTH 238 and 333.
If you liked discrete mathematics:
The natural sequel to Discrete Mathematics is MTH 254 or 255 and then 353. In addition, you may be interested in MTH 246 and in CSC 252 (counts 2 credits toward the mathematics major).
If you are interested in graduate school in mathematics:
Take a lot of courses, but be sure to take MTH 233, 254, and 281 and as many of MTH 264, 333, 370, 381, and 382 as possible. You should also consider taking a graduate course at the University of Massachusetts.
If you are interested in graduate school in statistics:
The MST Mathematical Statistics joint Major between MTH and SDS is explicitly designed as a preparation for graduate school in Statistics.
If you are interested in graduate school in operations research:
Operations research is a relatively new subarea of mathematics, bringing together mathematical ideas and techniques that are applied to large organizations such as businesses, computers, and governments. You should take MTH 211 and at least some of the courses listed for statistics above, some combinatorics (MTH 254) and some computer science. Consider also Topics in Applied Mathematics and Numerical Analysis.
If you want to be a teacher:
Certification requirements vary widely from state–to–state. If you are interested in teaching in secondary school, a mathematics major plus practice teaching may be enough to get started. In Massachusetts, the major should include either MTH 233 or 238 and one of MTH 220 or 246. A course involving geometry, such as MTH 270 or MTH 370 is also helpful. You should also have some introduction to computers. For guidelines, look at the list of courses listed in the MAT program. Finally, while MTH 307 Topics in Mathematics Education is rarely offered, something equivalent is taught as a special studies whenever there are MAT students.
If you are interested in teaching elementary school, most of your required courses will be in the education department. In the mathematics department, our concern would be that you are comfortable with mathematics, have seen its variety, and most important, that you enjoy it. For all that, you should take the mathematics courses which appeal to you most. For education courses, the latest information is that you should take EDC 235, 238, 346, 347, 404 (practice teaching), and one elective to be certified. Note that during the semester when you take practice teaching EDC 404, you will likely be unable to take a math course. Plan ahead and consult the education department.
If you want to be a doctor:
You are doing fine by majoring in mathematics. A course in statistics would be a very good idea. Other areas of mathematics that would be useful are differential equations and combinatorics.
If you want to be an actuary:
Take MTH 246, 290, 291 and 320 and the actuarial exams that are offered periodically. Advancement as an actuary is achieved by passing of a series of examinations. Informal student study groups often form (ask around!).
If you want to get a good job when you graduate:
A major in mathematics prepares you well, regardless of which courses you choose. Math majors learn to think on their feet; they aren't frightened of numbers and they're at home with abstract ideas. Often, this alone is what employers are looking for. That said, we should add that knowledge of computer programming is very useful, as is some familiarity with statistics.
If you want something Smith does not offer:
If you are interested in a subject we do not offer, you should talk to professors whose fields of interest are closest to the subject, as a special studies. The arrangement must be approved by the department, but reasonable requests are not refused. If your interest is particularly strong, you might consider an honors project, or summer research work. You should also consider taking a course (or courses) at one of the consortium schools.
Faculty
Opportunities & Resources
Postbaccalaureate Program
The Center for Women in Mathematics is a place for women to get intensive training at the advanced level and an opportunity to study in a community that is fun, friendly and serious about math. Build the skills and confidence needed to continue on to graduate school.
Contact Department of Mathematical Sciences
Clark Science Center
Smith College
Burton Hall 115
Northampton, MA 01063