Catalogue 2018-2019 [ARCHIVED CATALOG]
Mathematics and Statistics Department
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Chair: John McCleary;
Professors: Natalie Priebe Frank, Benjamin Lotto (and Dean of Studies), John McCleary, Charles Steinhorn;
Associate Professor: Ming-Wen An, Kariane Calta, Jan Cameronb;
Assistant Professors: Jingchen (Monika) Hua, Adam Lowrance, Benjamin Morina;
Visiting Assistant Professor: Moshe Cohen, Lisa Lowrance.
a On leave 2018/19, first semester
b On leave 2018/19, second semester
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, approximation methods, differential equations, sequences, and series. 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 or students who have completed MATH 101 or its equivalent.
Yearlong course sequence 121, MATH 126 /MATH 127 .
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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.
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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 or its equivalent.
First or second six-week course.
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MATH 131 - Numbers, Shape, Chance, and Change Semester Offered: Fall
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.
Would you like to see a more just and humane world? The SJQ courses engage you from the very start of your Vassar studies in thinking about the relationship between power and social change. A set of public lectures that address the nature of social justice accompany SJQ courses.
Two 50-minute periods and one 50-minute discussion period.
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MATH 132 - Mathematics and Narrative
1 unit(s)
To most, mathematics and narrative live in opposition-narrative is ubiquitous while mathematics is perceived as inscrutably esoteric and obscure. In fact, narrative is a fundamental part of mathematics. Mathematical proofs, problems and solutions, textbooks, and journal articles tell some sort of story. Conversely, many literary works (Arcadia, Proof, and Uncle Petros and the Goldbach Conjecture) use mathematics as an integral part of their narrative. Movie and television narratives such as Good Will Hunting and Numb3rs are also mathematically based. Nonfiction works about mathematics and mathematical biographies like Chaos, Fermat’s Enigma, and A Beautiful Mind provide further examples of the connection between mathematics and narrative. We use this course to explore this connection by reading and writing a variety of mathematical narratives.
Open only to first-year students; satisfies college requirement for a First-Year Writing Seminar.
Not offered in 2018/19.
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MATH 141 - Introduction to Statistical Reasoning Semester Offered: Fall
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 estimaation 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 used. Computationally less intensive than MATH 240 . Ming-Wen An, Jingchen Hu.
Prerequisite(s): Three years of high school mathematics.
Not open to students with AP credit in statistics or students who have completed MATH 240 , ECON 209 or PSYC 200 .
Not recommended for students who have taken a semester of calculus: those students should instead consider MATH 240 . AP Statistics, MATH 141 and MATH 240 all provide an introduction to statistics and students should not take more than one; they all can serve as a prerequisite for further statistics courses in the Mathematics and Statistics Department.
In certain semesters, one section may be cross-listed with BIOL 141 .
Three 50-minute periods.
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MATH 142 - Statistical Sleuthing: Personal and Public Policy Decision-Making in a World of Numbers
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. The department.
Open only to first-year students; satisfies the college requirement for a First-Year Writing Seminar.
Three 50-minute periods.
Not offered in 2018/19.
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.
Prerequisite(s): MATH 126 and MATH 127 or equivalent.
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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.
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MATH 228 - Methods of Applied Mathematics Semester Offered: Fall and 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.
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MATH 240 - Introduction to Statistics Semester Offered: 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. Ming-Wen An, Jingchen Hu.
Prerequisite(s): MATH 126 and 127 .
Three 50-minute periods.
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MATH 241 - Probability Semester Offered: Fall
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.
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MATH 242 - Applied Statistical Modeling Semester Offered: Fall
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 will be expected to conduct data analyses in R. The department.
Prerequisite(s): MATH 126 and MATH 127 ; MATH 141 .
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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.
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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.
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MATH 268 - Protecting Information: Applications of Abstract Algebra
1 unit(s)
In today’s information age, it is vital to secure messages against eavesdropping or corruption by noise. Our study begins by surveying some historical techniques and proceeds to examining some of the most important codes currently being used to protect information. These include various public key cryptographic schemes (RSA and its variants) that are used to safeguard sensitive internet communications, as well as linear codes, mathematically elegant and computationally practical means of correcting transmissions errors. The department.
Prerequisite(s): MATH 126 and MATH 127 , or permission of the department.
Not offered in 2018/19.
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MATH 290 - Field Work Semester Offered: Fall or Spring
0.5 to 1 unit(s)
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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.
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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.
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 - Senior Seminar Semester Offered: Spring
0.5 to 1 unit(s)
Areas of study and units of credit vary from year to year. The department.
Open only to seniors who have a declared major in mathematics. It is strongly recommended that MATH 361 be completed before enrolling in Mathematics 301.
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MATH 315 - Advanced Topics in Applied Mathematics Semester Offered: Spring
1 unit(s)
This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. We develop such equations from real-world examples and applications from physics, biology, epidemiology, and from student interests. We explore several mathematical and numerical strategies for solving these models and introduce ways to glean information from them. Students may also be exposed to a collection of non-standard mathematical modeling techniques: Cellular Automata, Pair Approximation Equations, and Agent Based Modeling. Familiarity with programming in Matlab is developed throughout the semester.
Prerequisite(s): MATH 220 , MATH 221 and MATH 228 .
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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.
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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.
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MATH 327 - Advanced Topics in Real Analysis
1 unit(s)
Continuation of MATH 321 . Measure theory, the Lebesgue integral, Banach spaces of measurable functions. The department.
Prerequisite(s): MATH 321 .
Not offered in 2018/19.
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MATH 328 - Theory of Differential Equations and Dynamical Systems
1 unit(s)
Existence and uniqueness theorems for ordinary differential equations; general theory and eigenvalue methods for first order linear systems. The department.
Prerequisite(s): MATH 321 or permission of the instructor.
Not offered in 2018/19.
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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.
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MATH 335 - Differential Geometry
1 unit(s)
The geometry of curves and surfaces in 3-dimensional space and an introduction to manifolds. The department.
Prerequisite(s): MATH 321 .
Not offered in 2018/19.
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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 .
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MATH 341 - Statistical Inference Semester Offered: Spring
1 unit(s)
An introduction to statistical theory through the mathematical development of topics including resampling methods, sampling distributions, likelihood, interval and point estimation, and introduction to statistical inferential methods. The department.
Prerequisite(s): MATH 220 , MATH 221 and MATH 241 .
Three 50-minute periods.
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MATH 342 - Applied Statistical Modeling Semester Offered: Fall
1 unit(s)
For students who have completed MATH 341 . Students in this course attend the same lectures as those in MATH 242 , but will be required to complete extra reading and problems. Ming-Wen An.
Prerequisite(s): MATH 220 , MATH 221 and MATH 341 .
Three 50-minute periods.
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MATH 347 - Bayesian Statistics Semester Offered: 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. Ming-Wen An, Jingchen Hu.
Prerequisite(s): MATH 220 , MATH 221 and MATH 241 .
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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 .
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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.
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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.
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MATH 367 - Advanced Topics in Modern Algebra
1 unit(s)
Continuation of MATH 361 . Rings and fields, with a particular emphasis on Galois theory. The department.
Prerequisite(s): MATH 361 .
Not offered in 2018/19.
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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.
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