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MATH0116A-S17

CRN: 22133

Intro to Statistical Science
Introduction to Statistical Science
A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0210 or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab.

MATH0116Z-S17

CRN: 22134

Intro to Statistical Science
Intro Statistical Science Lab
Introduction to Statistical Science
A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0210 or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab.

MATH0121B-S17

CRN: 20065

Calculus I
Calculus I
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc.

MATH0121C-S17

CRN: 21141

Calculus I
Calculus I
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc.

MATH0122A-S17

CRN: 21349

Calculus II
Calculus II
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc.

MATH0122B-S17

CRN: 20090

Calculus II
Calculus II
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc.

MATH0122C-S17

CRN: 21531

Calculus II
Calculus II
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc.

MATH0190A-S17

CRN: 21442

Math Proof: Art and Argument
Mathematical Proof: Art and Argument
Mathematical proof is the language of mathematics. As preparation for upper-level coursework, this course will give students an opportunity to build a strong foundation in reading, writing, and analyzing mathematical argument. Course topics will include an introduction to mathematical logic, standard proof structures and methods, set theory, and elementary number theory. Additional topics will preview ideas and methods from more advanced courses. We will also explore important historical examples of proofs, both ancient and modern. The driving force behind this course will be mathematical expression with a primary focus on argumentation and the creative process. (MATH 0122 or MATH 0200) 3 hrs. lect.

MATH0200A-S17

CRN: 20652

Linear Algebra
Linear Algebra
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc.

MATH0200B-S17

CRN: 21350

Linear Algebra
Linear Algebra
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc.

MATH0200C-S17

CRN: 20091

Linear Algebra
Linear Algebra
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc.

MATH0218A-S17

CRN: 22410

Statistical Learning
Statistical Learning
This course is an introduction to modern statistical, machine learning, and computational methods to analyze large and complex data sets that arise in a variety of fields, from biology to economics to astrophysics. The theoretical underpinnings of the most important modeling and predictive methods will be covered, including regression, classification, clustering, resampling, and tree-based methods. Student work will involve implementation of these concepts using open-source computational tools. (MATH 0116 and experience with at least one programming language) 3 hrs. lect./disc.

MATH0223A-S17

CRN: 20365

Multivariable Calculus
Multivariable Calculus
The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc.

MATH0223B-S17

CRN: 20653

Multivariable Calculus
Multivariable Calculus
The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc.

MATH0225A-S17

CRN: 22135

Topics in Linear Alg & Diff Eq
Topics in Linear Algebra and Differential Equations
Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc.

MATH0302A-S17

CRN: 21532

Abstract Algebra I
Abstract Algebra
Groups, subgroups, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, rings and ideals, integral domains and fields, the field of quotients of a domain, the ring of polynomials over a domain, Euclidean domains, principal ideal domains, unique factorization, factorization in a polynomial ring. (MATH 0200 or by waiver) 3 hrs. lect./disc.

MATH0325A-S17

CRN: 22137

Complex Analysis
Complex Analysis
An introduction to functions of a complex variable. Mappings of the complex plane, analytic functions, Cauchy Integral Theorem and related topics. (MATH 0223 or by waiver) 3 hrs. lect./disc.

MATH0328A-S17

CRN: 22411

Numerical Linear Algebra
Numerical Linear Algebra
Numerical linear algebra is the study of algorithms for solving problems such as finding solutions of linear systems and eigenvalues of matrices. Many real-life applications simplify to these scenarios and often involve millions of variables. We will analyze shortcomings of direct methods such as Gaussian Elimination, which theoretically produces the true solution but fails in practical applications. In contrast, iterative methods are often more practical and precise, and continually evolve with changing technology and our understanding of mathematics. Our study will include the First Order Richardson, Steepest Descent, and Conjugate Gradient algorithms for linear systems, and the power method for eigenvalue problems. (MATH 0200) 3 hrs. lect.

MATH0410A-S17

CRN: 22138

Stochastic Processes
Stochastic Processes
Stochastic processes are mathematical models for random phenomena evolving in time or space. This course will introduce important examples of such models, including random walk, branching processes, the Poisson process and Brownian motion. The theory of Markov chains in discrete and continuous time will be developed as a unifying theme. Depending on time available and interests of the class, applications will be selected from the following areas: queuing systems, mathematical finance (Black-Scholes options pricing), probabilistic algorithms, and Monte Carlo simulation. (MATH 0310) 3 hrs. lect./disc.

MATH0500A-S17

CRN: 20394

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500C-S17

CRN: 20382

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500D-S17

CRN: 20383

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500F-S17

CRN: 20385

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500G-S17

CRN: 20386

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500H-S17

CRN: 20388

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500I-S17

CRN: 20663

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500J-S17

CRN: 20830

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500K-S17

CRN: 20664

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500L-S17

CRN: 20997

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0500M-S17

CRN: 21627

Advanced Study
Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

MATH0704A-S17

CRN: 20134

Senior Seminar
Senior Seminar
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc.

MATH0745A-S17

CRN: 22396

Polynomial Method Seminar
The Polynomial Method
A tutorial in the Polynomial Method for students who have completed work in Abstract Algebra and at least one of Combinatorics, Graph Theory, and Number Theory. We will study Noga Alon’s Combinatorial Nullstellensatz and related theorems, along with their applications to combinatorics, graph theory, number theory, and incidence geometry. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. (Approval required; MATH 0302 and one of the following: MATH 0241, MATH 0247, or MATH 0345).

Department of Mathematics

Warner Hall
303 College Street
Middlebury College
Middlebury, VT 05753