## Courses

2015-2016

For the college’s course catalog, please visit the Courses section. For courses currently offered, please visit the Schedule of Classes.

MATH-102 Elements of Statistics

An introduction to statistical reasoning and methodology. Topics include experimental design, exploratory data analysis, elementary probability, a standard normal-theory approach to estimation and hypothesis testing and linear and multi-variable regression. Not open for credit to students who have taken Psychology 370. (Offered each year)

MATH-120 Special Topics in Mathematics

Variable topics involving: mathematical methods for the Natural and Social Sciences and Mathematical Problem Solving.

MATH-121 Essentials of Calculus

A one-semester introduction to single-variable differential and integral calculus and selected topics in multi-variable calculus. Emphasis is given to applications from the natural and social sciences. (Offered each semester)

MATH-122 Mathematical Methods for the Physical and Social Sciences

This course will explore three major topics of mathematics: linear algebra, probability and statistics, and Markov chains. Using these three topics, students will engage in three real world applications in biology, chemistry, and economics. This course is well suited for students who need a year of mathematics, like many pre-professional programs, and are looking for real applications of mathematics beyond the typical algebra and calculus approach. While this course would be a natural extension for pre-professional students who have take Math 121 Essentials of Calculus, this course only requires a strong background in high school Algebra II.

MATH-123 Calculus I (Single Variable)

An accelerated introduction to the calculus of single variable functions. Topics include limits, derivatives, integrals, and applications of calculus to the natural and social sciences. Prerequisite: Placement or Math 121. (Offered each semester)

MATH-124 Calculus II (Multivariable)

A continuation of the study of single variable calculus, together with an introduction to linear algebra and the calculus of multivariable functions. Topics include: an introduction to infinite sequences and series, vectors, partial and directional derivatives, gradient, optimization of functions of several variable, integration techniques, double integrals, elementary linear algebra, and an introduction to differential equations with applications to the physical and social sciences. Prerequisite: AP Calculus AB or BC score of 4 or 5 or Math 123. (offered each semester)

MATH-199 Introductory Topics in Mathematics

A general category used only in the evaluation of transfer credit.

MATH-200 Topics in Mathematics

(Also listed under Computer Science offerings.)

MATH-210 Introduction to Proof Techniques

An introduction to proof writing techniques. Topics will include logic and proofs, set theory, mathematical induction, relations, modular arithmetic, functions, cardinality, number theory, and calculus. Prerequisite: Math 124 or combination of MATH 123 and CS 173. (Offered each semester)

MATH-215 Technical Communication I

This course aims to enhance mathematics and computer science students' proficiency and comfort in orally communicating content in their disciplines. Students will present three talks during the semester on substantive, well-researched themes appropriate to their status in their major. Prerequisite: Math 210 or CS 271. (Offered each year)

MATH-231 Linear Algebra and Differential Equations

A continued study of Linear Algebra with applications to linear differential equations and mathematical models in the physical and social sciences. Topics include abstract vector spaces over the real and complex numbers, bases and dimension, change of basis, the Rank-Nullity Theorem, orthogonal bases, linear transformations, the matrix of a linear transformation, eigenvectors and eigenvalues, diagonalization, the matrix exponential, linear differential equations of order n, linear systems of first order differential equations, and a continued study of infinite series, power series, and series solutions of linear differential equations. Prerequisite: Math 124. (Offered each semester)

MATH-232 Mathematical Modeling

A course in mathematical modeling including linear and nonlinear optimization models, linear and non-linear dynamic models, and probability and statistical models. Both continuos and discrete models are considered. This course focuses on applying mathematics to open ended, real world problems, and effectively communicating conclusions. Sensitivity analysis and model robustness are emphasized throughout. This course also strongly features approximation and simulation methods along side analytic methods. Prerequisite: MATH 231. (Offered each spring)

MATH-242 Applied Statistics

Statistics is the science of reasoning from data. This course will introduce you to the fundamental concepts and methods of statistics, including calculus-based probability. Topics include experimental design, data collection, and the scopes of conclusion, a robust study of probability models and their application to statistical inference, hypothesis testing, and regression analysis. Prerequisite: Math 124. (Offered each fall)

MATH-275 Elementary Graph Theory

Graphs are mathematical structures that are used to model a great variety of phenomena ranging from the internet to social networks to phylogenetic clusters, In this class, we will study the mathematical properties of graphs and develop algorithms to solve many common graph problems. Prerequisite: CS 109 or 110 or 111 and 174 or MATH 210. (Offered each spring)

MATH-299 Intermediate Topics in Mathematics

A general category used only in the evaluation of transfer credit.

MATH-315 Technical Communication II

This course is a capstone experience in oral and written communication for mathematics and computer science majors. Students will research a substantive topic, write a rigorous expository article, and make a presentation to the department. Prerequisite: Math/CS 215. Corequisite: a 300-400 level mathematics or computer science course. (Offered each semester)

MATH-321 Advanced Analysis

A rigorous analysis of limits, continuity, differentiation, integration, uniform convergence, infinite series and basic topology. Prerequisites: Math 210, 231. (Offered every other fall)

MATH-322 Topology

A study of general topological spaces, including interiors, closures, boundaries, subspace, product, and quotient topologies, continuous functions, homeomorphisms, metric spaces, connectedness, and compactness together with applications of these concepts. Additional topics may include algebraic topology, including homotopy and homology groups, and/or a parallel study of general measure spaces, including inner and outer measure. Prerequisite: Math 321 or permission of instructor. (Offered every other spring)

MATH-329 Complex Analysis

An introduction to complex numbers, analytic functions, derivatives, singularities, integrals, Taylor series, Laurent Series, conformal mappings, residue theory, analytic continuation. Cauchy-Riemann Equations, Cauchy's Theorem, Cauchy Integral Formula, Big and Little Picard Theorems, Riemann Mapping Theorem, Rouche's Theorem. Prerequisite: Math 210, 231. (Offered every other year)

MATH-331 Combinatorics

In this course, we will study counting techniques for discrete collections of objects. This course will include topics such as permutations and combinations, binomial coefficients, inclusion-exclusion, Fibonacci numbers, Catalan numbers, set partitions, Stirling numbers, generating functions, exponential generating functions, and Pólya counting. Prerequisite: Math 210.

MATH-332 Abstract Algebra

A rigorous analysis of the structure and properties of abstract groups, rings, fields, and vector spaces. Prerequisites: Math 210, 231. (Offered every other fall)

MATH-334 Theory of Computation

This course is a study of formal languages and their related automata, Turing machines, unsolvable problems and NP-complete problems. Prerequisites: CS 109 or 110 or CS 111 and Math 210 or CS 174.

MATH-337 Operations Research

This course involves mathematical modeling of real-world problems and the development of approaches to find optimal (or nearly optimal) solutions to these problems. Topics include: Modeling, Linear Programming and the Simplex Method, the Karush-Kuhn Tucker conditions for optimality, Duality, Network Optimization, and Nonlinear Programming. Prerequisite: Math 231. (Offered every other fall)

MATH-341 Applied Probability

A study of single variable, multi-variable, and stochastic probability models with application to problems in the physical and social sciences. Includes problems in Biology, Finance, and Computer Science. Prereqs: Math 231.

MATH-357 Vector Calculus and Fourier Analysis

After covering some important and applied Multivariable Calculus topics that were not covered in Math 124, this course will focus on Fourier Analysis, which is a widely used and applied subfield of advanced linear algebra (which also uses Calculus). For example, your ear processes a sound wave (maybe from plucking guitar strings) by changing into an orthogonal frequency basis allowing us to hear the main notes and some selected overtones. We will essentially use the power of changing (orthogonal) bases to analyze a wide array of problems in image processing, signal reconstruction, medical imaging, wave analysis, heat diffusion, statistical modeling, quantum mechanics, number theory, and geometry. No knowledge of these application topics is necessary. Prerequisite: Math 231.

MATH-361 Directed Study

MATH-362 Directed Study

MATH-363 Independent Study

MATH-364 Independent Study

MATH-399 Advanced Topics in Mathematics

A general category used only in the evaluation of transfer credit.

MATH-400 Advanced Mathematical Topics

Advanced topics in Abstract Algebra, Analysis, Geometry or Applied Math.

MATH-401 Advanced Mathematical Topics

Advanced topics in Abstract Algebra, Analysis, Geometry or Applied Math.

MATH-451 Senior Research

MATH-452 Senior Research