Catalogue 2022-2023 [ARCHIVED CATALOG]
Mathematics and Statistics Department
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Chair: Benjamin Lotto;
Professors: Natalie Priebe Frank, Benjamin Lotto, John McCleary;
Associate Professors: Ming-Wen An, Kariane Calta, Jan Cameronab, Jingchen (Monika) Hu, Adam Lowrance;
Assistant Professors: Andrew Borum, Lee Kennedy-Shaffera, Benjamin Morin;
Lecturer: Lisa Lowrance;
Visiting Assistant Professor: Qiaofeng Zhu;
Postdoctoral Fellow: Simon Hoellerbauer;
Research Professor: Charles Steinhorn;
Adjunct Professor: Jules Albertini;
Adjunct Assistant Professor: Hudson Gould (and Director of the Quantitative Research Center);
Adjunct Instructor: Barbara Dolansky.
a On leave 2022/23, first semester
ab On leave 2022/23
AP: Students receiving one unit of AP credit based on either the AB or BC Mathematics AP Examination or the calculus credit examination administered by the Department of Mathematics may not be granted credit for MATH 121 . Students receiving one unit of AP credit based on the Statistics AP Examination may not be granted credit for MATH 141 .
Advanced Course Placement: The department recommends that students who have earned a 4 or 5 on the BC examination enroll in MATH 220 . Students with a 5 on the AB examination or a 3 on the BC examination generally are advised to elect MATH 220 also, after conferring with the department. Students with a 4 on the AB examination ordinarily are advised to enroll in MATH 127 but should consult with the department.
Major
Correlate Sequence in Mathematics
Mathematics and Statistics: I. Introductory
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MATH 121 - Single Variable Calculus Semester Offered: Fall
1 unit(s)
The calculus of one variable and its applications are discussed. Topics include: limits, continuity, derivatives, applications of derivatives, transcendental functions, the definite integral, applications of definite integrals. The Department.
Prerequisite(s): A minimum of three years of high school mathematics, preferably including trigonometry.
Mathematics 121 is not open to students with AP credit in mathematics.
Course Format: CLS -
MATH 126 - Calculus IIA: Integration Theory Semester Offered: Fall and Spring
0.5 unit(s)
In this course, we expand and build upon basic knowledge of differential and integral calculus. Various techniques and applications of integration will be studied. The calculus of transcendental functions—such as the exponential, logarithmic, and inverse trigonometric functions—will also be developed. A main theme in this course is the many ways functions can be defined, and arise naturally in problems in the mathematical sciences.
Prerequisite(s): MATH 121 or its equivalent.
First or second six-week course.
Course Format: CLS -
MATH 127 - Calculus IIB: Sequences and Series Semester Offered: Fall and Spring
0.5 unit(s)
Real numbers may be represented as infinite decimals. In this course we generalize this representation by studying the convergence of sequences and of series of real numbers. These notions further generalize to the convergence of sequences and series of functions. We study these ideas and their relation to the Calculus.
Prerequisite(s): MATH 121 /MATH 126 or their equivalent.
First or second six-week course.
Course Format: CLS -
MATH 131 - Numbers, Shape, Chance, and Change Semester Offered: Fall or Spring
1 unit(s)
What is the stuff of mathematics? What do mathematicians do? Fundamental concepts from arithmetic, geometry, probability, and the calculus are explored, emphasizing the relations among these diverse areas, their internal logic, their beauty, and how they come together to form a unified discipline. As a counterpoint, we also discuss the “unreasonable effectiveness” of mathematics in describing a stunning range of phenomena from the natural and social worlds. The Department.
Prerequisite(s): At least three years of high school mathematics.
Open only to first-year students; satisfies the college requirement for a First-Year Writing Seminar.
Three 50-minute periods.
Course Format: CLS -
MATH 141 - Introduction to Statistical Reasoning Semester Offered: Fall or Spring
1 unit(s)
The purpose of this course is to develop an appreciation and understanding of the exploration and interpretation of data. Topics include exploratory data analysis, basic probability, design of studies, and inferential methods including confidence interval estimation and hypothesis testing. Applications and examples are drawn from a wide variety of disciplines. When cross-listed with biology, examples are drawn primarily from biology. Statistical software is introduced and used. Computationally less intensive than MATH 240 .
Prerequisite(s): Three years of high school mathematics.
Not open to students with AP credit in statistics or students who have completed ECON 209 or PSYC 200 : those students should instead consider MATH 242 . Not recommended for students who have taken a semester of calculus: those students should instead consider MATH 240 .
In certain semesters, one section may be cross-listed with BIOL 141 .
Course Format: CLS -
MATH 142 - Statistical Sleuthing: Personal and Public Policy Decision-Making in a World of Numbers Semester Offered: Fall and Spring
1 unit(s)
The world inundates us with numbers and pictures intended to persuade us towards certain beliefs about our health, public policy, or even which brand of product to buy. How can we make informed decisions in this context? The goal of this course is for us to become statistical sleuths who critically read and summarize a piece of statistical evidence. We read articles from a variety of sources, while using basic statistical principles to guide us. Course format: mixture of discussion and lecture, with regular reading and writing assignments.
Open only to first-year students; satisfies the college requirement for a First-Year Writing Seminar.
Three 50-minute periods.
Course Format: CLS -
MATH 144 - Foundations of Data Science Semester Offered: Fall
1 unit(s)
(Same as CMPU 144 ) This course focuses on the development and practice of computational and inferential thinking. Students are introduced to the fundamentals of programming and inference. Students learn to write programs, create data visualizations, and work with real-world datasets, culminating in a final data analysis project.
Course Format: CLS
Mathematics and Statistics: II. Intermediate
Prerequisites for all intermediate courses: MATH 126 and MATH 127 , or permission of the department, unless otherwise indicated.
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MATH 220 - Multivariable Calculus Semester Offered: Fall and Spring
1 unit(s)
This course extends differential and integral calculus to functions of several variables. Topics include: partial derivatives, gradients, extreme value problems, Lagrange multipliers, multiple integrals, line and surface integrals, the theorems of Green and Gauss. The Department.
Prerequisite(s): MATH 126 and MATH 127 or equivalent.
Course Format: CLS -
MATH 221 - Linear Algebra Semester Offered: Fall and Spring
1 unit(s)
The theory of higher dimensional space. Topics include: geometric properties of n-space, matrices and linear equations, vector spaces, linear mappings, determinants. The Department.
Prerequisite(s): MATH 126 and MATH 127 or equivalent, or permission of the department.
Course Format: CLS -
MATH 228 - Methods of Applied Mathematics Semester Offered: Spring
1 unit(s)
Survey of techniques used in the physical sciences. Topics include: ordinary and partial differential equations, series representation of functions, integral transforms, Fourier series and integrals. The Department.
Prerequisite(s): MATH 126 and MATH 127 , or permission of the department.
Course Format: CLS -
MATH 240 - Introduction to Statistics Semester Offered: Fall or Spring
1 unit(s)
The purpose of this course is to introduce the methods by which we extract information from data. Topics are similar to those in MATH 141 , with more coverage of probability and more intense computational and computer work. Statistical software is introduced and used. Ming-Wen An, Jingchen Hu.
Prerequisite(s): MATH 126 and MATH 127 (or the equivalent).
Corequisite(s): Not open to students with AP credit in statistics or students who have completed MATH 141 : those students should instead consider MATH 242 . Students who have completed ECON 209 or PSYC 200 should consult the instructor about appropriate placement.
Three 50-minute periods.
Course Format: CLS -
MATH 241 - Probability Semester Offered: Fall and Spring
1 unit(s)
This course in introductory probability theory covers topics including combinatorics, discrete and continuous random variables, distribution functions, joint distributions, independence, properties of expectations, and basic limit theorems. The Department.
Prerequisite(s): MATH 126 and MATH 127 , or permission of the department.
Course Format: CLS -
MATH 242 - Applied Statistical Modeling Semester Offered: Fall or Spring
1 unit(s)
Applied Statistical Modeling is offered as a second course in statistics in which we present a set of case studies and introduce appropriate statistical modeling techniques for each. Topics may include: multiple linear regression, logistic regression, log-linear regression, survival analysis, an introduction to Bayesian modeling, and modeling via simulation. Other topics may be substituted for these or added as time allows. Students are expected to conduct data analyses in R.
Prerequisite(s): MATH 126 and MATH 127 (or the equivalent); and AP credit in statistics, MATH 141 or MATH 240 .
Course Format: CLS -
MATH 261 - Introduction to Number Theory Semester Offered: Fall and Spring
1 unit(s)
Topics include: divisibility, congruence, modular arithmetic, diophantine equations, number-theoretic functions, distribution of the prime numbers. The Department.
Prerequisite(s): MATH 126 and MATH 127 , or permission of the department.
Course Format: CLS -
MATH 263 - Discrete Mathematics Semester Offered: Spring
1 unit(s)
Mathematical induction, elements of set theory and logic, permutations and combinations, relations, topics in graph theory, generating functions, recurrence relations, Boolean algebras. The Department.
Prerequisite(s): MATH 126 and MATH 127 , or permission of the department.
Course Format: CLS -
MATH 280 - Intermediate Data Science Semester Offered: Spring
1 unit(s)
(Same as CMPU 280 ) This course develops additional core skills in data science, with a key focus on machine learning and with a wide array of applications in different fields. It emphasizes computation over statistics, although the statistical intuition is still covered. Topics covered may include regression, clustering, classification, supervised and unsupervised machine learning, and non-standard data objects such as text data and network data. The course uses both Python and R and covers version control using Git.
A weekly laboratory period provides guided hands-on experience. Marc Smith.
Prerequisite(s): CMPU 144 or MATH 144 ; CMPU 101 and either MATH 141 or MATH 240 ; or permission of the instructor.
Two 75-minute periods and one 2-hour lab.
Course Format: CLS -
MATH 290 - Community-Engaged Learning Semester Offered: Fall or Spring
0.5 to 1 unit(s)
Course Format: INT -
MATH 297 - Topics in Mathematics Semester Offered: Fall
0.5 unit(s)
Reading Course
Prerequisite(s): MATH 221 or equivalent, and permission of the instructor.
Course Format: OTH -
MATH 298 - Independent Work Semester Offered: Fall or Spring
0.5 to 1 unit(s)
Election should be made in consultation with a department adviser.
Course Format: OTH
Mathematics and Statistics: III. Advanced
Prerequisites for all advanced courses: MATH 220 and MATH 221 , or permission of the department, unless otherwise indicated.
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MATH 301 - Topics In Advanced Mathematics and Statistics Semester Offered: Fall and Spring
0.5 to 1 unit(s)
The focus of the intensive is proposed by the faculty leader and based on student’s previous studies. Students take an active role in presentation and research throughout the semester in collaboration with the faculty leader. Topics may come from mathematics, statistics, and applications of mathematics. The Department.
Prerequisite(s): MATH 220 , 221 and permission of the instructor.
Open only to declared majors in mathematics.
Course Format: INT -
MATH 315 - Advanced Topics in Applied Math Semester Offered: Fall
1 unit(s)
Using informal, but careful, mathematical approaches we analyze nonlinear equations that arise from a wide variety of applied fields. Methods developed include analytical approaches as well as a geometric understanding of the underlying dynamics. We move from understanding 1-dimensional nonlinear flow to 2-D dynamics in the phase plane. Atop of a typical single variable calculus class, we are employing skills such as function sketching, Taylor series expansions, partial derivatives, Jacobian matrix, divergence theorem, eigenvalues, and eigenvectors. Benjamin Morin.
Prerequisite(s): MATH 220 , MATH 221 , MATH 228 .
Three 50-minute periods.
Course Format: CLS -
MATH 317 - Numerical Analysis Semester Offered: Spring
1 unit(s)
This course serves as an introduction to computational methods for a variety of problems that cannot be solved analytically. Topics covered include finding roots of polynomials, interpolation, numerical integration & solutions of differential equations, and various matrix computations (e.g., eigenvalues). We study the construction of these algorithms from a formal standing and analyze them with an eye to accuracy, efficiency, and stability. Students use MATLAB to explore the algorithms in a hands on way to assess the validity and implementation of the methods developed. Benjamin Morin Andy Borum
Prerequisite(s): MATH 220 , MATH 221 , and MATH 228 .
Three 50-minute periods.
Course Format: CLS -
MATH 321 - Real Analysis Semester Offered: Fall and Spring
1 unit(s)
A rigorous treatment of topics in the classical theory of functions of a real variable from the point of view of metric space topology including limits, continuity, sequences and series of functions, and the Riemann-Stieltjes integral. The Department.
Prerequisite(s): For all advanced courses: MATH 220 and MATH 221 , unless otherwise indicated.
Course Format: CLS -
MATH 324 - Complex Analysis Semester Offered: Spring
1 unit(s)
Integration and differentiation in the complex plane. Topics include: holomorphic (differentiable) functions, power series as holomorphic functions, Taylor and Laurent series, singularities and residues, complex integration and, in particular, Cauchy’s Theorem and its consequences. The Department.
Prerequisite(s): For all advanced courses: MATH 220 and MATH 221 , unless otherwise indicated.
Course Format: CLS -
MATH 331 - Topics in Geometry Semester Offered: Fall
1 unit(s)
Topics vary from year to year and may include differential geometry, fractal geometry, Euclidean geometry, hyperbolic geometry, projective geometry, and algebraic geometry.
Prerequisite(s): MATH 220 and MATH 221 , unless otherwise indicated.
Course Format: CLS -
MATH 339 - Topology Semester Offered: Spring
1 unit(s)
Introductory point-set and algebraic topology; topological spaces, metric spaces, continuous mappings, connectedness, compactness and separation properties; the fundamental group; simplicial homology. The Department.
Prerequisite(s): MATH 321 or MATH 361 .
Course Format: CLS -
MATH 341 - Statistical Inference Semester Offered: Fall or Spring
1 unit(s)
An introduction to the theory behind statistical inference methods. Topics include point and interval estimation, sampling distributions, sufficient statistics, hypothesis testing, exposure to Bayesian inference, and simulation.
Prerequisite(s): AP credit in statistics, MATH 141 or MATH 240 ; MATH 220 , MATH 221 , and MATH 241 .
Course Format: CLS -
MATH 347 - Bayesian Statistics Semester Offered: Fall or Spring
1 unit(s)
An introduction to Bayesian statistics. Topics include Bayes Theorem, common prior and posterior distributions, hierarchical models, Bayesian linear regression, latent variable models, and Markov chain Monte Carlo methods. The course uses R extensively for simulations.
Prerequisite(s): AP credit in statistics, MATH 141 or MATH 240 ; MATH 220 , MATH 221 , and MATH 241 .
Course Format: CLS -
MATH 348 - Statistical Principles for Research Study Design Semester Offered: Fall or Spring
1 unit(s)
Research studies are used in many fields, from economics and political science to physics, biology, and medical research. All of them share a need for statistically valid methods for study design and the analysis of results. This course covers the statistical principles and challenges behind randomized and non-randomized studies in these and other fields, highlighting the role statisticians play in the research process. Mathematical theory, examples, and simulations in R are considered in evaluating study designs.
Prerequisite(s): AP credit in statistics, MATH 141 or MATH 240 ; MATH 220 , MATH 221 , and MATH 241 .
Course Format: CLS -
MATH 351 - Mathematical Logic Semester Offered: Fall
1 unit(s)
An introduction to mathematical logic. Topics are drawn from computability theory, model theory, and set theory. Mathematical and philosophical implications also are discussed. The Department.
Prerequisite(s): MATH 321 or MATH 361 .
Course Format: CLS -
MATH 361 - Modern Algebra Semester Offered: Fall and Spring
1 unit(s)
The theory of groups and an introduction to ring theory. Topics in group theory include: isomorphism theorems, generators and relations, group actions, Sylow theorems, fundamental theorem of finite abelian groups. The Department.
Prerequisite(s): for all advanced courses: MATH 220 and MATH 221 , unless otherwise indicated.
Course Format: CLS -
MATH 364 - Advanced Linear Algebra Semester Offered: Fall
1 unit(s)
Further study in the theory of vector spaces and linear maps. Topics may include: scalar products and dual space; symmetric, hermitian and unitary operators; eigenvectors and eigenvalues; spectral theorems; canonical forms. The Department.
Prerequisite(s): for all advanced courses: MATH 220 and MATH 221 , unless otherwise indicated.
Course Format: CLS -
MATH 382 - Statistical Machine Learning Semester Offered: Fall or Spring
1 unit(s)
Machine learning methods address problems of making predictions from data. This course expands on prior study of data visualization and estimation and introduces methods of supervised and unsupervised learning, model training, and validation. Students are expected to engage in statistical programming in R to apply these methods to data.
Prerequisite(s): AP credit in statistics, MATH 141 or MATH 240 ; plus MATH 220 , MATH 221 , and MATH 241 .
Course Format: CLS -
MATH 383 - Optimization Methods Semester Offered: Fall or Spring
1 unit(s)
This course focuses on optimization problems — methods for minimizing and maximizing functions. Topics might include linear, nonlinear, and/or integer programming. We focus on the formulation of optimization problems, characterizing minima and maxima, and numerical methods for computing them. As we cover these topics, we also consider applications of optimization in a variety of areas.
Prerequisite(s): MATH 220 and MATH 221 .
Course Format: CLS -
MATH 399 - Senior Independent Work Semester Offered: Fall or Spring
0.5 to 1 unit(s)
Election requires the approval of a departmental adviser and of the instructor who supervises the work.
Course Format: OTH
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