Middlebury

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MATH0116A-S15

CRN: 22151

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.

MATH0116B-S15

CRN: 22152

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.

MATH0116Y-S15

CRN: 22153

Intro to Statistical Science
Discussion
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-S15

CRN: 22154

Intro to Statistical Science
Discussion
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.

MATH0121A-S15

CRN: 20063

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.

MATH0121B-S15

CRN: 20068

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-S15

CRN: 21253

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-S15

CRN: 21543

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-S15

CRN: 20093

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-S15

CRN: 22144

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-S15

CRN: 21875

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-S15

CRN: 20702

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-S15

CRN: 21544

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-S15

CRN: 20094

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.

MATH0223A-S15

CRN: 20392

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-S15

CRN: 20703

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.

MATH0228A-S15

CRN: 22544

Intro to Numerical Analysis
Introduction to Numerical Analysis
We will study the development, analysis, and implementation of numerical methods for approximating solutions to mathematical problems. We will begin with applications of Taylor polynomials, computer representation of numbers, and types of errors. Other topics will include polynomial and spline interpolation, numerical integration and differentiation, rootfinding, and numerical solutions of differential equations. Accuracy will be quantified by the concept of numerical error. Additionally, we will study the stability, efficiency, and implementation of algorithms. We will utilize the software MATLAB throughout to demonstrate concepts, as well as to complete assignments and projects. (MATH 0200)

MATH0241A-S15

CRN: 22146

Elementary Number Theory
Elementary Number Theory
Divisibility and prime factorization. Congruences; the theorems of Lagrange, Fermat, Wilson, and Euler; residue theory; quadratic reciprocity. Diophantine equations. Arithmetic functions and Mobius inversion. Representation as a sum of squares. (MATH 0122 or by waiver)

MATH0302A-S15

CRN: 22145

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-S15

CRN: 22147

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.

MATH0345A-S15

CRN: 22148

Combinatorics
Combinatorics
Combinatorics is the “art of counting.” Given a finite set of objects and a set of rules placed upon these objects, we will ask two questions. Does there exist an arrangement of the objects satisfying the rules? If so, how many are there? These are the questions of existence and enumeration. As such, we will study the following combinatorial objects and counting techniques: permutations, combinations, the generalized pigeonhole principle, binomial coefficients, the principle of inclusion-exclusion, recurrence relations, and some basic combinatorial designs. (MATH 0200 or by waiver) 3 hrs. lect./disc.

MATH0410A-S15

CRN: 22149

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.

MATH0423A-S15

CRN: 22150

Topics in Analysis
Topics in Analysis
In this course we will study advanced topics in real analysis, starting from the fundamentals established in MA401. Topics may include: basic measure theory; Lebesgue measure on Euclidean space; the Lebesgue integral; total variation and absolute continuity; basic functional analysis; fractal measures. (MATH 0323 or by waiver) 3 hrs. lect./disc.

MATH0500A-S15

CRN: 20433

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.

MATH0500B-S15

CRN: 20139

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-S15

CRN: 20421

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-S15

CRN: 20422

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.

MATH0500E-S15

CRN: 20423

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-S15

CRN: 20425

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-S15

CRN: 20427

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-S15

CRN: 20713

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-S15

CRN: 20714

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-S15

CRN: 21079

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-S15

CRN: 22458

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-S15

CRN: 20140

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.

Department of Mathematics

Warner Hall
303 College Street
Middlebury College
Middlebury, VT 05753