The Senior Capstone Experience in mathematicsconsists of two components: a senior thesis andeither an oral presentation of the thesis in frontof the faculty and majors at seminar, or a posterpresentation. Comprehensive exams may be offeredin place of a traditional senior thesis. TheSenior Capstone Experience in mathematics isgraded as Pass, Fail, or Honors. Students must doa thesis and make an oral presentation to earn thegrade of honors.

This course is an introduction to the rapidlydeveloping science of complexity. It is adiscussion of the tools-fractals, chaos, andself-organization-being refined for the purpose ofunderstanding such things as the fractured andirregular structures of Nature, surprise andunpredictability, and the emergence of lifelikeproperties from inanimate matter. The theme of thecourse is that complexity can arise from simpleorigins, such as the repeated application ofelementary processing rules. The course emphasizesthe use of the computer for visualization.Practical application of these ideas in medicineand engineering will be discussed, as willexamples of the connections between complexity inthe sciences and that in the humanities and thearts.

Linear programming, matrices, sets and counting,Markov process, difference equations, and graphs.The course emphasizes developing, analyzing,and interpreting mathematical models.

This course is designed for students in theElementary Education Certification Program and forstudents planning to complete the SecondaryEducation Certification Program in an area otherthan mathematics. The framework of the courseconsists of four themes: Number Systems and theirOperations, Algebra and Functions, Geometry andMeasurement, Data Analysis, Statistics, andProbability. Emphasis throughout is on reasoningand problem-solving using concepts and proceduresfrom all four areas. Substantial amounts of bothreading and writing is required and students areexpected to demonstrate both orally and in writinga thorough understanding of the concepts and theability to communicate this understanding toothers.

Analytic geometry, the derivative anddifferential, elementary functions, limits,continuity, and applications. This course is part1 (of 2) of a yearlong sequence in differentialcalculus. At the end of this two-course sequence,students tackle all the topics above included indifferential calculus. Completion of thisyear-long sequence is equivalent to completion ofMAT 111: Differential Calculus. Please note,Pre-Calculus placement score must be less than 50to take this course. Also note, MAT 106 and MAT107 can be counted as a two-course quantitativesequence for distribution, but MAT 106 and 107 donot count as a quantitative course otherwise.

This course is the second semester of a year-longsequence in Differential Calculus. Topics in thiscourse include trigonometry, derivatives oftrigonometric functions, conic sections, implicitdifferentiation, and limits at infinity. Thesemester concludes with the Fundamental Theorem ofCalculus. Throughout the semester, students workon a project involving Calculus, culminating in afinal paper and a presentation. Completion of thisyear-long sequence is equivalent to completion ofMAT 111: Differential Calculus. Also note, MAT 106and MAT 107 can be counted as a two-coursequantitative sequence for distribution, but MAT106/107 does not count as a quantitative courseotherwise.

Introduction to the theory and practice of dataanalysis and statistics in the natural and socialsciences. Statistical software will be used.Topics will include data ethics, sampling,experimental design, descriptive statistics,conditional probability, the normal distribution,simple linear regression, confidence intervals,hypothesis tests, and decisions.

Analytic geometry, the derivative anddifferential, elementary functions, limits,continuity, and applications. Prerequisite: It isstrongly recommended that a student should havestrong algebra and trigonometric skills beforetaking this course.

The indefinite integral, the definite integral,the fundamental theorem of the integral calculus,sequences, series, and applications.

Topics not regularly offered in a department'snormal course offerings, chosen based on currentstudent interest and faculty expertise. Specialtopic courses can only be offered 3 times; afterthis, the course must be approved as a regularcourse. Graded A-F or Pass/Fail.

An agreement between a sponsoring faculty memberand a student researching a topic of interest thatis relevant to a student's major or minor.Research is conducted on campus. Students must beenrolled before the research can begin. GradedA-F or Pass/Fail. 45 hours are required percredit.

An agreement between a sponsoring faculty memberand a student researching a topic of interest thatis relevant to a student's major or minor.Research is conducted off-campus. Students must beenrolled before the research can begin. Graded A-For Pass/Fail. 45 hours are required per credit.

An agreement between a sponsoring faculty and astudent letting the student study a topic ofinterest not offered at WC. 45 hours are requiredper credit.

A continuation of the theory and practice of dataanalysis and statistics in the natural and socialsciences. Use of statistical software constitutesa significant part of this course. Commonstatistical mistakes and the careful and ethicalapplication of statistical methods are emphasized.Topics include experimental design, multivariatelinear regression, non-parametric and parametricinference, power calculations, logisticregression, chi-squared tests, and ANOVA.

Vectors, partial derivatives, and multipleintegrals for functions of several variables. Lineand surface integrals.

The heart of data science is going from a delugeof numbers to ever-elusive insight. In thisintroduction we focus on first principles: askinggood questions, being aware of our assumptions,and understanding what it means to do goodscience. Topics include exploratoryanalysis/descriptive statistics, statisticaltesting, and data visualization. The courseconcludes with an introduction to recentdata-driven machine learning models. We discussethical issues pertaining to data and machinelearning throughout the course, using currentevents and articles as they arise. The course isboth math and programming intensive, although in aheavily applied manner.

A critical study of the basic concepts ofgeometry. This course begins with an axiomaticapproach to Euclidean geometry which includescareful proofs of its principal theorems. Thecourse will continue with an examination ofvarious types of non-Euclidean geometries whichmay include spherical geometry, projectivegeometry, and/or hyperbolic geometry.

An introduction to logic, reasoning, and thediscrete mathematical structures that areimportant in computer science. Topics includeproposition logic, types of proof, induction andrecursion, sets, combinatorics, functions,relations, and graphs.

This course serves as a focused introduction toprogramming for scientists and engineers. Topicsinclude algorithm development, statistical tests,the fast Fourier transform (FFT), simulating thedynamics of systems represented by coupledordinary differential equations (e.g. planetarymotion via Runge-Kutta methods), numericalintegration, root finding, fitting functions toexperimental data, and the creation ofpublication-quality graphics. Students choose andcomplete an independent research project on atopic related to their major. This course enablesstudents to integrate computation into advancedcourses in theoretical and/or experimentalscience. Programming language: Python.

An introduction to linear algebra balancingcomputation and the reading, understanding, andwriting of mathematical proofs. A selection oftopics from systems of linear equations, matrices,vector spaces, bases, dimension, lineartransformations, determinants, eigenvalues, changeof basis, matrix representations of lineartransformations, matrix decompositions, andapplications of linear algebra. It is recommendedthat students take MAT 240 before this course.

Topics not regularly offered in a department'snormal course offerings, chosen based on currentstudent interest and faculty expertise. Specialtopic courses can only be offered 3 times; afterthis, the course must be approved as a regularcourse. Graded A-F or Pass/Fail.

An agreement between a sponsoring faculty memberand a student researching a topic of interest thatis relevant to a student's major or minor.Research is conducted on campus. Students must beenrolled before the research can begin. GradedA-F or Pass/Fail. 45 hours are required percredit.

An agreement between a sponsoring faculty memberand a student researching a topic of interest thatis relevant to a student's major or minor.Research is conducted off-campus. Students must beenrolled before the research can begin. Graded A-For Pass/Fail. 45 hours are required per credit.

An agreement between a sponsoring faculty and astudent letting the student study a topic ofinterest not offered at WC. 45 hours are requiredper credit.

Elementary methods for the solution of ordinarydifferential equations, including the expansion ofthe solution in an infinite series.

Events and their probabilities, dependence, andindependence. Bayes Theorem. Variates and expectedvalues. Theorems of Bernoulli and De Moivre.Special distributions. Central limit theorem andapplications.

Theory of functions of a complex variable,including applications to problems in the theoryof functions of a real variable. Cauchy's IntegralFormula and its application to the calculus ofresidues.

This course introduces techniques forapproximating solutions to various mathematicalproblems that are either computationallychallenging or impossible to solve via directmethods. Topics to be covered include erroranalysis, interpolation and extrapolation,numerical differentiation and integration, anditerative methods for solving systems of equationsand eigenvalue problems.

This course introduces elementary combinatorialtechniques used to enumerate large but finitediscrete sets, including some of the following:permutations, the binomial theorem, partitions,bijections, and well-known sequences. It alsopresents the fundamentals of graph theory: trees,networks, paths and connectivity, matchings,colorings, and optimization algorithms. There is asignificant proof-writing component pluscomputations and opportunities for coding.

This course tackles challenges that arise in thefunctioning (operations) of a complexorganization, and then works to formulate,analyze, and solve corresponding mathematicaldecision models. Some of these challenges mightinvolve distributing tasks among processescompeting for limited resources, arrangingtransportation between hubs to minimize cost, orscheduling employees' shifts to meet demands whilelowering payroll costs. We develop mathematicaland computational tools, understand how they work,and explore some of their historic usage inindustry. Topics include some combination of:linear programming & the simplex method;transportation & assignment problems; networkmodels; dynamic programming; integer programming.

Factorization of integers. Congruences and residueclasses. Theorems of Euler, Fermat, Wilson, andGauss. Primitive roots. Quadratic residues and thereciprocity theorem.

A learning contract is developed prior toenrollment in an internship. Evaluation of studentperformance is completed by the faculty mentorbased on the fulfillment of the contract terms andwritten evaluation by the internship sitesupervisor. Students must work at least 45 hoursfor each internship credit and be enrolled in thecourse prior to beginning work. Graded A-F orPass/Fail.

Open to mathematics majors only. Weekly meetingsof the majors and faculty in the department arescheduled to provide information about careers,graduate school, thesis topics, and researchareas, as well as to prepare each major to makepresentations of problem solutions and to make therequired presentation on the thesis. All juniormathematics majors are enrolled in the seminar andwill receive a pass/fail grade at the end of thesemester. Junior standing, and permission of theDepartment.

Open to mathematics majors only. Weekly meetingsof the majors and faculty in the department arescheduled to provide information about careers,graduate school, thesis topics, and researchareas, as well as to prepare each major to makepresentations of problem solutions and to make therequired presentation on the thesis. All juniormathematics majors are enrolled in the seminar andwill receive a pass/fail grade at the end of thesemester. Junior standing, and permission of theDepartment.

Topics not regularly offered in a department'snormal course offerings, chosen based on currentstudent interest and faculty expertise. Specialtopic courses can only be offered 3 times; afterthis, the course must be approved as a regularcourse. Graded A-F or Pass/Fail.

An agreement between a sponsoring faculty memberand a student researching a topic of interest thatis relevant to a student's major or minor.Research is conducted on campus. Students must beenrolled before the research can begin. GradedA-F or Pass/Fail. 45 hours are required percredit.

An agreement between a sponsoring faculty memberand a student researching a topic of interest thatis relevant to a student's major or minor.Research is conducted off-campus. Students must beenrolled before the research can begin. Graded A-For Pass/Fail. 45 hours are required per credit.

An agreement between a sponsoring faculty and astudent letting the student study a topic ofinterest not offered at WC. 45 hours are requiredper credit.

Introduction to groups, rings and fields. Othertopics may include integral domains, polynomialrings, and fields.

A rigorous treatment of single-variable calculus.A selection of topics from the properties and thetopology of the real numbers, sequences, series,continuity, differentiation, and Riemannintegration.

A continuation of Real Analysis II. Topicsselected according to student and instructorinterest. Topics could include analysis in metricspaces, analysis in n-dimensional space, Fourieranalysis, functional analysis, measure theory, andLebesgue integration. Suitable for engineers,chemists, physicists, economists, andmathematicians.

A learning contract is developed prior toenrollment in an internship. Evaluation of studentperformance is completed by the faculty mentorbased on the fulfillment of the contract terms andwritten evaluation by the internship sitesupervisor. Students must work at least 45 hoursfor each internship credit and be enrolled in thecourse prior to beginning work. Graded A-F orPass/Fail.

Open to mathematics majors only. Senior studentsmake a presentation of a preliminary outline oftheir capstone project in the fall semester andpresent a report on the completed capstoneproject in the spring. All senior mathematicsmajors are enrolled in the seminar and receive apass/fail grade at the end of the semester.

Open to mathematics majors only. Senior studentsmake a presentation of a preliminary outlineof their capstone project in the fall semester andpresent a report on the completed capstone projectin the spring. All senior mathematics majors areenrolled in the seminar and receive a pass/failgrade at the end of the semester.

Topics not regularly offered in a department'snormal course offerings, chosen based on currentstudent interest and faculty expertise. Specialtopic courses can only be offered 3 times; afterthis, the course must be approved as a regularcourse. Graded A-F or Pass/Fail.

An agreement between a sponsoring faculty memberand a student researching a topic of interest thatis relevant to a student's major or minor.Research is conducted on campus. Students must beenrolled before the research can begin. GradedA-F or Pass/Fail. 45 hours are required percredit.

An agreement between a sponsoring faculty memberand a student researching a topic of interest thatis relevant to a student's major or minor.Research is conducted off-campus. Students must beenrolled before the research can begin. Graded A-For Pass/Fail. 45 hours are required per credit.

An agreement between a sponsoring faculty and astudent letting the student study a topic ofinterest not offered at WC. 45 hours are requiredper credit.