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MATH0100A-F17

CRN: 92485

A World of Mathematics
A World of Mathematics
How long will oil last? What is the fairest voting system? How can we harvest food and other resources sustainably? To explore such real-world questions we will study a variety of mathematical ideas and methods, including modeling, logical analysis, discrete dynamical systems, and elementary statistics. This is an alternative first mathematics course for students not pursuing the calculus sequence in their first semester. The only prerequisite is an interest in exploring contemporary issues using the mathematics that lies within those issues. (Approval required; This course is not open to students who have had a prior course in calculus or statistics.) 3 hrs lect./disc.

MATH0116A-F17

CRN: 91744

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-F17

CRN: 91745

Intro to Statistical Science
Intro Stats 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.

MATH0121A-F17

CRN: 90124

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-F17

CRN: 90131

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-F17

CRN: 91423

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-F17

CRN: 90155

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-F17

CRN: 90165

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-F17

CRN: 90166

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.

MATH0200A-F17

CRN: 90169

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-F17

CRN: 90170

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-F17

CRN: 90918

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.

MATH0200D-F17

CRN: 91804

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.

MATH0216A-F17

CRN: 91838

Introduction to Data Science
Introduction to Data Science
In this course students will gain exposure to the entire data science pipeline: forming a statistical question, collecting and cleaning data sets, performing exploratory data analyses, identifying appropriate statistical techniques, and communicating the results, all the while leaning heavily on open source computational tools, in particular the R statistical software language. We will focus on analyzing real, messy, and large data sets, requiring the use of advanced data manipulation/wrangling and data visualization packages. Students will be required to bring their own laptops as many lectures will involve in-class computational activities. (MATH 0116; or ECON 0210 or PSYC 0201 and experience with R) 3 hrs lect./disc.

MATH0223A-F17

CRN: 90219

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-F17

CRN: 92350

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-F17

CRN: 92352

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)

MATH0247A-F17

CRN: 92353

Graph Theory
Graph Theory
A graph (or network) is a useful mathematical model when studying a set of discrete objects and the relationships among them. We often represent an object with a vertex (node) and a relation between a pair with an edge (line). With the graph in hand, we then ask questions, such as: Is it connected? Can one traverse each edge precisely once and return to a starting vertex? For a fixed k/, is it possible to “color” the vertices using /k colors so that no two vertices that share an edge receive the same color? More formally, we study the following topics: trees, distance, degree sequences, matchings, connectivity, coloring, and planarity. Proof writing is emphasized. (MATH 0122 or by waiver) 3 hrs. lect./disc.

MATH0302A-F17

CRN: 91836

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.

MATH0310A-F17

CRN: 91545

Probability
Probability
An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications. (concurrent or prior MATH 0223 or by waiver) 3 hrs. lect./disc.

MATH0318A-F17

CRN: 92354

Operations Research
Operations Research
Operations research is the utilization of quantitative methods as an aid to managerial decisions. In the course, several of these methods will be introduced and studied in both a mathematical context and a physical context. Topics included will be selected from the following: classification of problems and the formulation of models, linear programming, network optimization, transportation problems, assignment problems, integer programming, nonlinear programming, inventory theory, and game theory. (MATH 0200 or waiver)

MATH0323A-F17

CRN: 90220

Real Analysis
Real Analysis
An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc.

MATH0500A-F17

CRN: 90227

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-F17

CRN: 90579

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-F17

CRN: 90446

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-F17

CRN: 90694

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-F17

CRN: 90698

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-F17

CRN: 90699

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-F17

CRN: 90819

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-F17

CRN: 90820

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-F17

CRN: 91669

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.

MATH0703A-F17

CRN: 92341

Finite Fields Seminar
Finite Fields Seminar
This course is a tutorial in the theory and applications of finite fields, which lie in the intersection of algebra and number theory. Working in small groups, students will study the fundamental structure and properties of finite fields (also known as Galois fields). They will then work independently, exploring applications in cryptography, coding theory, or other areas. Students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0241 or MATH 0302; Approval required) 3 hrs. Sem

MATH0704A-F17

CRN: 91837

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