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The two ARC courses listed below do not satisfy area or distribution credit.

12303

ARC 150 Algebra Workshop

Maria Belk

. T . . .

7:00 – 9:00 pm

RKC 115

N/A

(2 credits) This course provides a review of the algebra used in math, science, and social science courses. It is designed for students who would like to improve their algebra skills while taking or in preparation to take an introductory math, science, economics or statistics course. Topics include linear equations and their graphs, quadratic equations, fractions, rational expressions, and exponents. This course meets for the first ten weeks of the semester, and it will be graded Pass/Fail. No distributional credit is earned. Class Size: 20

12304

ARC 190 Algebra, Trigonometry

and Functions

Maria Belk

. . W . .

7:00 – 9:00 pm

RKC 115

N/A

(2 credits) This course is designed for students who have taken a pre-calculus course in high school or at Bard, but would like more computational practice with algebra, trigonometry, logarithms and exponentials. This course can be taken at the same time as a math, science, or economics course, or in preparation to take such a course in a subsequent semester. This course meets for the first ten weeks of the semester, and will be graded Pass/Fail. No distributional credit is earned. Class size: 20

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12195

MATH 119 Chance

Samuel Hsiao

M . W . .

10:10 - 11:30 am

HEG 204

MATC

The mathematical theory of probability is useful for quantifying the uncertainty that we face in everyday life. This course introduces basic ideas in discrete probability and explores a wide range of practical applications such as evaluating medical diagnostic tests, courtroom evidence, and data from surveys. We will use algebra as a problem-solving tool throughout this course. Prerequisite: passing score on Part I of the Mathematics Diagnostic. Class size: 24

12196

MATH 131 Exploration in Number Theory

Lauren Rose

. T . Th .

10:10 - 11:30 am

HEG 308

MATC

This course will provide an overview of one of the oldest and most beautiful areas of mathematics. It is ideal for any student who wants a taste of mathematics outside of the calculus sequence. Topics may include: number puzzles, prime numbers, congruences, quadratic reciprocity, sums of squares, Diophantine equations, cryptography, coding theory, and continued fractions. Prerequisite: Precalculus or the equivalent. Class size: 24

12197

MATH 141 A Calculus I

James Belk

M . W . .

11:50 -1:10 pm

RKC 115

MATC

An introduction to the basic ideas of differentiation and integration in one variable. Topics include limits, techniques of differentiation, definite integrals, the fundamental theorem of calculus, and applications. Prerequisite: Precalculus or the equivalent. Class size: 24

12198

MATH 141 B Calculus I

Maria Belk

M . W . .

3:10 -4:30 pm

RKC 115

MATC

See above. Class size: 24

12199

MATH 142 A Calculus II

Jennie D'Ambroise

. T . Th .

10:10 - 11:30 am

HEG 204

MATC

This course, a continuation of Calculus I, reinforces the fundamental ideas of the derivative and the definite integral. Topics covered include techniques of integration, l'Hopital's rule, improper integrals, applications of integration, functions of several variables, partial derivatives, multiple integrals. Prerequisites: Mathematics 141 or the equivalent. Class size: 24

12200

MATH 142 B Calculus II

Jennie D'Ambroise

. T . Th .

11:50 -1:10 pm

HEG 204

MATC

See above. Class size: 24

12201

MATH 212 Calculus III

Cliona Golden

. T . Th .

8:30 -9:50 am

HEG 102

MATC

This course investigates differentiation and integration of multivariable functions. Topics covered include vectors, coordinate systems, vector valued functions, partial derivatives, gradients, Lagrange multipliers, multiple integrals, change of variables, line integrals, Green’s theorem, and Stokes’ theorem. Prerequisite: Mathematics 142 or the equivalent. Class size: 24

12202

MATH 213A Linear Algebra with

Ordinary Differential Equations

Ethan Bloch

M . W . .

1:30 -2:50 pm

HEG 102

MATC

This course is an introduction to two fields of mathematics, linear algebra and ordinarydifferential equations, that are of fundamental importance throughout mathematics and itsapplications, and that are related by the important use of linear algebra in the study of systemsof linear differential equations. Topics in linear algebra include n-dimensional Euclidean space, vectors, matrices, systems of linear equations, determinants, eigenvalues and eigenvectors; topics in ordinary differential equations include graphical methods, separable differential equations, higher order linear differential equations, systems of linear differential equations andapplications. Prerequisite: Mathematics 142 or the equivalent. Class size: 20

12203

MATH 213B Linear Algebra with

Ordinary Differential Equations

John Cullinan

. T . Th .

10:10 - 11:30 am

HEG 106

MATC

See above. Class size: 20

12205

MATH 261 Proofs and Fundamentals

Gregory Landweber

M . . . .

. . W . .

10:10 - 11:30 am

9:10 - 11:30 am

HEG 308

MATC

This course introduces students to the methodology of mathematical proof. The logic of compound and quantified statements, mathematical induction, and basic set theory including functions and cardinality are covered. Topics from foundational mathematics are developed to provide students with an opportunity to apply proof techniques. Prerequisite: Mathematics 142, or permission of instructor. Note that this is a writing intensive course. We will devote an extra hour each week to a writing lab, where we will work on writing both mathematical proofs and mathematics papers. . Class size: 15

12206

MATH 301 Numerical Analysis Lab

Gregory Landweber

M . W . .

11:50 -1:10 pm

RKC 100

MATC

This course is an introduction to mathematical computation. After reviewing Taylor series and introducing algorithms for finding the zeros of non-linear functions, solving linear systems quickly, and approximating eigenvectors and eigen values, the bulk of the course will be devoted to curve fitting by means of polynomial interpolation, splines, bezier curves, and least squares. Other topics may include matrix factorizations, the Page Rank algorithm, sparse matrices, and vector processing. The course will be equal parts programming with Sage, a mathematical computation package built on Python, and discussion of the theory underlying the algorithms. Corequisite: Mathematics 213 or Mathematics 242, and any Computer Science course or basic programming experience. Class size: 15

12207

MATH 319 Probability and Statistics

Samuel Hsiao

M . W . .

1:30 -2:50 pm

HEG 204

MATC

Everyday we make decisions based on numerical data in the face of uncertainty. We do so while reading the latest political polls, playing a card game, interpreting a medical diagnosis, or analyzing a scientific experiment. Probabilistic models and statistical methods help us to think through such decisions in a precise mathematical fashion. This course provides a calculus-based introduction to techniques and applications of probability and statistics. Topics considered will include random variables and their distributions, the Central Limit Theorem, hypothesis testing. Prerequisites: Math 212. Some knowledge of Linear Algebra is helpful. For students concentrating in economics, Math 319 can substitute for Economics 229. Class size: 15

12208

MATH 324 Fourier Analysis & Wavelets

Cliona Golden

. T . Th .

11:50 -1:10 pm

HEG 102

MATC

Over the past few decades, signal processing has gone through a mathematical revolution. Traditionally, signal processing was built on the Fourier transform, a mathematical tool that is used to express signals as superpositions of pure sinusoidal functions. While the Fourier transform is well suited to understanding physical phenomena, such as waves, it does not have the flexibility to effectively analyze more complicated functions, such as speech signals or natural images. A relatively new mathematical tool, called the wavelet transform, has now become the staple of many important signal processing tasks ranging from image compression

to denoising. This course will introduce the mathematical foundations of the Fourier and the wavelet transforms, with excursions into signal processing. Prerequisite: Mathematics 212 and Mathematics 213 or Mathematics 242. Class size: 15

12209

MATH 332 Abstract Algebra

Lauren Rose

. T . Th .

1:30 -2:50 pm

HEG 204

MATC

An introduction to modern abstract algebraic systems, including groups, rings, fields and vector spaces. The course will focus primarily on a rigorous treatment of the basic theory of groups (subgroups, quotient groups, homomorphisms, isomorphisms, group actions) and vector spaces (subspaces, bases, dimension, linear maps). Prerequisite: Mathematics 261, and Mathematics 213 or 242, or permission of the instructor. Class size: 15

12210

MATH 361 Real Analysis

James Belk

M . W . .

3:10 -4:30 pm

RKC 102

MATC

The fundamental ideas of analysis in one-dimensional Euclidean space are studied. Topics covered include the completeness of the real numbers, sequences, Cauchy sequences, continuity, uniform continuity, the derivative, and the Riemann integral. As time permits other topics may be considered, such as infinite series of functions or metric spaces. Prerequisite: Mathematics 261 and one prior 300-level mathematics course is recommended, or permission of the instructor.

Class size: 15

12211

MATH 362 Complex Analysis

Jennie D'Ambroise

. . W . F

10:10 - 11:30 am

HEG 102

MATC

This course will cover the basic theory of functions of one complex variable. Topics will include the geometry of complex numbers, holomorphic and harmonic functions, Cauchy’s theorem and its consequences, Taylor and Laurent series, singularities, residues, elliptic functions and/or other topics as time permits. Prerequisite: Mathematics 212, Mathematics 261, and one prior 300-level mathematics course is recommended, or permission of the instructor. Class size: 15

12212

MATH 417 Algebraic Number Theory

John Cullinan

. T . Th .

1:30 -2:50 pm

RKC 101

MATC

In this course we will study algebraic number fields (finite extensions of the rational numbers) from an algebraic and an analytic viewpoint, motivated by the special cases of quadratic and cyclotomic fields. The goal of the course is to develop an understanding of the deep connections between algebra, analysis, and arithmetic. Topics will include: rings of integers, factorization, ideal class group, unit group, zeta and L-functions, Dirichlet's theorem. Prerequisite: Mathematics 332

Class size: 12