Mathematics and Statistics

101f    Calculus with Pre-calculus I     Designed for students who enter Colby with insufficient pre-calculus background for the standard calculus sequence. It is expected that all students who complete Mathematics 101 will enroll in Mathematics 102 in the following January. The combination of 101 and 102 covers the same calculus material as Mathematics 121. Completion of 101 alone does not constitute completion of a College calculus course for any purpose; in particular, it does not qualify a student to take Mathematics 122 nor does it satisfy the quantitative reasoning requirement. Students electing this course must complete the mathematics placement questionnaire prior to registration. Three credit hours.    RHODES

102j    Calculus with Pre-calculus II    A continuation of Mathematics 101. Successful completion of both Mathematics 101 and 102 is equivalent to completion of Mathematics 121. Prerequisite: Mathematics 101. Three credit hours.  Q.    RHODES

110f    Statistical Thinking    An introduction to basic concepts in statistics with a focus on statistical literacy. Students will learn practical applications and the language and reasoning involved in analyzing data including the use of statistical software. Topics include graphical and numerical methods for summarizing data, central tendency, variability, introductory probability, designing experiments and collecting data, and evaluating data from experiments, studies, and surveys. Does not count toward any major or minor. Credit may be received for only one of Mathematics 110, 212, or 231. Four credit hours.  Q.    SCOTT

111s    Mathematics as a Liberal Art    The historical and contemporary role of mathematics in culture and intellectual endeavor; the nature of contemporary mathematics; mathematics as a tool for problem solving; logical reasoning; selected topics from modern mathematics. Four credit hours.  Q.    TAYLOR

121fs    Single-Variable Calculus    Differential and integral calculus of one variable: limits and continuity; differentiation and its applications, antiderivatives, the definite integral and its applications; exponential, logarithmic, and trigonometric functions. Students electing this course in the fall term must complete the mathematics placement questionnaire prior to registration. Four credit hours.  Q.    FACULTY

122fs    Series and Multi-Variable Calculus     Further study of calculus of one and several variables: infinite series, vectors and analytic geometry in two and three dimensions, partial derivatives, multi-variable calculus. Prerequisite: A course in single-variable calculus. Four credit hours.  Q.    FACULTY

161f    Honors Calculus I    The first course in the honors calculus sequence. A synthesized approach to the calculus of one and several variables presented as a deductive mathematical theory, with emphasis on concepts, theorems, and their proofs. May not be taken for credit if the student has earned credit for Mathematics 122. First-year students must complete the mathematics placement questionnaire before selecting this course. Prerequisite: One year of calculus in high school. Four credit hours.  Q.    MATHES

162s    Honors Calculus II    A continuation of Mathematics 161. Integral calculus of several variables, infinite series. May not be taken for credit if the student has earned credit for Mathematics 122. Prerequisite: Mathematics 161. Four credit hours.    MATHES

212fs    Introduction to Statistical Methods     A first course in statistical methods for scientists. Addresses issues for proposing/designing an experiment as well as exploratory and inferential techniques for analyzing and modeling scientific data. Topics include descriptive statistics, design of experiments, randomization, elementary probability, random variables, discrete and continuous probability distributions, contingency tables, measures of association for categorical variables, confidence intervals, one- and two-sample tests of hypotheses for means and proportions, analysis of variance, correlation/regression, logistic regression, nonparametrics. Statistical computing packages will be used throughout. Credit may be received for only one of Mathematics 110, 212, or 231. Four credit hours.  Q.    O'BRIEN

231fs    Applied Statistics and Regression Analysis    Elementary probability theory, special discrete and continuous distributions, descriptive statistics, sampling theory, confidence intervals, tests of hypotheses, correlation, linear regression, and multiple linear regression. Examples and applications slanted toward economics. Credit may be received for only one of Mathematics 110, 212, or 231. Prerequisite: Mathematics 102, 121, or 161. Four credit hours.  Q.    SCOTT

253fs    Linear Algebra    Solutions of linear systems of equations, matrix algebra, determinants. Introduction to abstract vector spaces and linear transformations, eigen values, and eigenvectors. Prerequisite: Mathematics 102, 121, 122, or 161. Four credit hours.    BRETSCHER, GOUVEA, LIVSHITS, MATHES

274fs    Introduction to Abstract Mathematical Thought     An introduction to fundamental mathematical techniques used in upper-level mathematics courses. Presents the principles of mathematical logic and uses them to examine standard methods of direct and indirect proof, including mathematical induction. Topics include techniques from finite mathematics, the set theoretic approach to functions and relations, and the theory of infinite sets. Credit can be received for only one of Mathematics 274 and 275. Prerequisite: Mathematics 102, 121, 122, or 161. Two semesters of calculus is recommended. Four credit hours.    LIVSHITS, MATHES

275s    Introduction Topics in Abstract Mathematics    An independent study of introductory topics in abstract mathematics used in upper-level mathematics courses. Topics include the set-theoretic approach to functions and relations, the theory of infinite sets, elementary algebraic structures, and techniques from discrete mathematics. Credit can be received for only one of Mathematics 274 and 275. Prerequisite: Mathematics 161 and 162 and permission of the department. Two credit hours.    MATHES

302fs    Vector Calculus    An advanced calculus course. Vectors, lines, and planes; limits, continuity, derivatives, and integrals of vector-valued functions; polar, spherical, and cylindrical coordinates; partial and directional derivatives; multiple integrals; line and surface integrals; Green's Theorem; Stokes's Theorem; Fourier series; applications. Typically involves the use of a large computer mathematics package such as Mathematica or Maple. Prerequisite: Mathematics 122 or 162. Four credit hours.    BRETSCHER, TAYLOR

311fs    Introduction to Differential Equations    Theory and solution methods of ordinary differential equations; linear differential equations; first-order linear systems; qualitative behavior of solutions; nonlinear dynamics; existence and uniqueness of solutions; applications. Prerequisite: Mathematics 122 or 162, and 253. Four credit hours.    HOLLY

[312]    Partial Differential Equations    An introduction to partial differential equations. Linear and nonlinear partial differential equations, systems; initial value problems, boundary value problems; analytic and numerical methods of solution; applications. Prerequisite: Mathematics 253 and 311. Four credit hours.    

[313]    Differential Geometry    An introduction to the differential geometry of curves and surfaces in three-dimensional space. Curves: tangent, normal, and binormal vectors; curvature and torsion; the moving frame. Surfaces: the first and second fundamental forms, the Theorema Egregium, sectional and Gaussian curvature, and selected additional topics. Prerequisite: Mathematics 122 or 162, and 253, and 274 or 275. Four credit hours.    

[331]    Topology     Point-set, differential, and algebraic topology. Prerequisite: Mathematics 274 or 275. Four credit hours.    

[332]    Introductory Numerical Analysis    Solution by numerical methods of linear and nonlinear equations, systems of equations, and differential equations; numerical integration; polynomial approximation; matrix inversion; error analysis. Prerequisite: Mathematics 122 or 162, and 253. Four credit hours.    

333f    Abstract Algebra    Introduction to algebraic structures, such as groups, rings, integral domains, and fields. Prerequisite: Mathematics 253, and 274 or 275. Four credit hours.    GOUVEA

336f    Mathematical Economics    Listed as Economics 336. Prerequisite: Economics 224, Mathematics 253, and either Mathematics 122 or 162. Four credit hours.    VULETIN

338s    Real Analysis    An introduction to real analysis, with special focus on foundational issues. Prerequisite: Mathematics 122 or 162, and 274 or 275. Four credit hours.    LIVSHITS

352f    Complex Variables    The arithmetic and calculus of complex numbers and functions. The properties of analytic functions, including Cauchy's integral theorem and formula, representation by Laurent series, residues and poles, and the elementary functions. Offered in alternate years. Prerequisite: Mathematics 122 or 162, and 274 or 275. Four credit hours.    LIVSHITS

357s    Elementary Number Theory    An introduction to the theory of numbers. Factorization and primes: unique factorization, greatest common divisors, the sequence of primes, primality testing and factoring on the computer, connections with cryptography. Congruences: linear congruences, theorems of Fermat, Euler, and Wilson, Chinese remainder theorem, quadratic residues, quadratic reciprocity law. Further topics chosen by the instructor. Offered in alternate years. Prerequisite: Mathematics 102, 121, 131, or 161. Two semesters of calculus or Mathematics 253 is recommended. Four credit hours.    GOUVEA

372f    Mathematical Modeling    Application of mathematics to real-life problems in a variety of areas. Interpretation of existing mathematical models, analysis, and computer simulation. Formulation and development of mathematical models. Prerequisite: Mathematics 122 or 162, and 253. Four credit hours.    HOLLY

[374]    Design and Analysis of Experiments    Methods of designing and analyzing scientific experiments to address research questions. Emphasis on statistical thinking and applications as much as underlying mathematical structures and theory. Topics include completely randomized factorial designs, randomized block designs, Latin squares, factorial designs, and fractional factorial designs. Computer applications are integrated throughout. Formerly offered as Mathematics 398A. Prerequisite: Mathematics 212, 231, or 382. Four credit hours.    

[376]    History of Mathematics    A survey of the history of mathematics since the dawn of civilization. Original sources will be examined. The instructor may choose to focus on one theme or topic and its development throughout the history of mathematics. Prerequisite: Mathematics 274 or 275. Four credit hours.  H.    

378s    Introduction to the Theory of Computation    Listed as Computer Science 378. Prerequisite: Computer Science 231 and either Mathematics 274 or 275. Four credit hours.    SKRIEN

381f    Mathematical Statistics I: Probability    A first course in probability covering axiomatic foundations, combinatorics, random variables, discrete and continuous probability distributions, special probability distributions, independence, conditional and marginal probability distributions, properties of expectations, moment generating functions, sampling distributions, weak and strong laws of large numbers, and the central limit theorem. Prerequisite: Mathematics 122 or 162. Four credit hours.    O'BRIEN

382s    Mathematical Statistics II: Inference     An introduction to statistical inference covering method of moments and maximum likelihood estimation, sample properties of estimators including sufficiency, consistency, and relative efficiency, Rao-Blackwell theorem, tests of hypotheses, confidence intervals, linear models, analysis of variance, and regression. Although applications are discussed the emphasis is on theory. Prerequisite: Mathematics 381. Four credit hours.    O'BRIEN

[391]    Problem-Solving Seminar     Seminar on problem solving designed for students of all levels. The focus is on mathematical puzzles and curiosity-driven mathematics. The goal is to explore systematic ways in which nonstandard problems can be approached. Facts and strategies presented will be of value to both pure and applied pursuits. Nongraded. One credit hour.    

398s    Topics in Epidemiology     Epidemiology is the study of the distribution and determinants of disease in human populations. An introduction to the central concepts of the field, highlighting the role of epidemiology in the context of public health. The focus is on descriptive and analytic epidemiology; measures of disease occurrence (incidence and prevalence) and association (the odds ratio, relative risk, and attributable risk); observational and experimental study designs; and interaction, confounding, and bias. The epidemiology of several diseases will be explored. Additional topics may include outbreak investigations, causal inference, clinical epidemiology, and basic survival analysis. Prerequisite: Mathematics 212 or 231 or 382. Four credit hours.    SCOTT

434s    Topics in Abstract Algebra    A sequel to Mathematics 333. Topics may vary from year to year. May be repeated, with permission of instructor, for credit. Prerequisite: Mathematics 333. Four credit hours.    GOUVEA

439f    Topics in Real Analysis    A sequel to Mathematics 338. Content may vary from year to year, but topics such as topology, measure theory, functional analysis, or related areas may be considered. May be repeated for credit with permission of instructor. Prerequisite: Mathematics 338. Four credit hours.    MATHES

484s    Honors Independent Study    The independent study component of the honors program in mathematics. Cannot be counted toward the major or minor. Prerequisite: Permission of the instructor and admission to the honors program. Three or four credit hours.    FACULTY

491f, 492s    Independent Study    Independent study in an area of mathematics of particular interest to the student. Prerequisite: Permission of the instructor. One to four credit hours.    FACULTY