Mathematics and Statistics Courses

Mathematics and Statistics | Courses | Faculty

The Department offers courses in mathematics and statistics for students with various interests and mathematical backgrounds. MATH 100 is a basic mathematics course which satisfies the General Education R1 requirement; it is not a pre-calculus course. The courses numbered 011, 101, 102, 103, and 104 are intended to assist the student in preparation for an introductory calculus course. MATH 127-128 is a calculus sequence for business and life and social science students. MATH 131-132 and MATH 135-136 are calculus sequences for students in fields such as mathematics, physics, chemistry, computer science, and engineering.

(All courses carry 3 credits unless otherwise noted.)

Mathematics

011 Elementary Algebra (R1) (both sem) (cr not applicable toward graduation)

Beginning algebra enhanced with pre-algebra topics such as arithmetic, fractions, and word problems as need indicates. Topics include real numbers, linear equations and inequalities in one variable, polynomials, factoring, algebraic fractions, problem solving, systems of linear equations, rational and irrational numbers, and quadratic equations.

012 Elementary Algebra (R1) (for Stock-bridge students) (both sem)

3 Stockbridge graduation credits, but 3 non-graduation University credits.

Beginning algebra enhanced with preal-gebra topics and word problems of particular interest to Stockbridge students. Topics include real numbers, linear equations and inequalities in one variable, polynomials, factoring, algebraic fractions, problem solving, systems of linear equations, rational and irrational numbers, and quadratic equations.

100 Basic Mathematics Skills for the Modern World (R1) (both sem)

Topics in mathematics that every educated person needs to know to process, evaluate, and understand the numerical and graphical information in our society. Applications of mathematics in problem solving, finance, probability, statistics, geometry, population growth. Note: This course does not cover the algebra and pre-calculus skills needed for calculus.

101 Precalculus Algebra with Functions and Graphs (both sem) 2 cr

First semester of the two-semester sequence MATH 101-102. Detailed, in-depth review of manipulative algebra; introduction to functions and graphs, including linear, quadratic, and rational functions. Prerequisite: MATH 011 or Placement Exam Part A score above 10. Students needing a less extensive review should register for MATH 104.

102 Analytic Geometry and Trigonometry (R1) (both sem) 2 cr

Second semester of the two-semester sequence MATH 101-102. Detailed treatment of analytic geometry, including conic sections and exponential and logarithmic functions. Same trigonometry as in MATH 104. Prerequisite: MATH 101.

103 Precalculus Trigonometry (1st sem) 1 cr

The trigonometry topics of MATH 104. Prerequisite: the equivalent of the algebra and geometry portions of MATH 104. (See also MATH 101, 102, 104.)

104 Algebra, Analytic Geometry, and Trigonometry (R1) (both sem)

One-semester review of manipulative algebra, introduction to functions, some topics in analytic geometry, and that portion of trigonometry needed for calculus. Prerequisite: MATH 011 or Placement Exam Part A score above 15. Students with a weak background should take the two-semester sequence MATH 101-102.

112 Finite Mathematics

Topics chosen from: properties of sets; counting techniques (e.g., permutations, combinations); finite differences; the mathematics of finance (e.g., compound interest, annuities, amortization); recursive patterns and relations; iteration; properties of algorithms; linear programming; properties of matrices; and characteristics and applications of finite graphs and trees. Prerequisite: working knowledge of high school algebra.

113 Mathematics for Elementary Teachers I (R2) (both sem)

Fundamental and relevant mathematics for prospective elementary school teachers, including whole numbers and place value operations with whole numbers, number theory, fractions, ratio and proportion, decimals, and percents. For Pre-Early Childhood and Pre-Elementary Education majors only. Prerequisite: MATH 011 or satisfaction of R1 requirement.

114 Mathematics for Elementary Teachers II (2nd sem)

Various topics that might enrich an elementary school mathematics program, including probability and statistics, the integers, rational and real numbers, clock arithmetic, diophantine equations, geometry and transformations, the metric system, relations and functions. For Pre-Early Childhood and Pre-Elementary Education majors only. Prerequisite: MATH 113.

121 Linear Methods and Probability for Business (R2) (both sem)

Linear equations and inequalities, matrices, linear programming with applications to business, probability and discrete random variables. Prerequisite: working knowledge of high school algebra and plane geometry.

127 Calculus for the Life and Social Sciences I (R2) (both sem)

Basic calculus with applications to problems in the life and social sciences. Functions and graphs, the derivative, techniques of differentiation, curve sketching, maximum-minimum problems, exponential and logarithmic functions, exponential growth and decay, and introduction to integration. Prerequisite: proficiency in high school algebra, including word problems. Honors sections available.

128 Calculus for the Life and Social Sciences II (R2) (both sem)

Continuation of MATH 127. Elementary techniques of integration, introduction to differential equations, applications to several mathematical models in the life and social sciences, partial derivatives, and some additional topics. Prerequisite: MATH 127.

131 Calculus I (R2) (both sem) 4 cr

Continuity, limits, and the derivative for algebraic, trigonometric, logarithmic, exponential, and inverse functions. Applications to physics, chemistry, and engineering. Students expected to have and use a Texas Instruments 86 graphics, programmable calculator. Prerequisites: high school algebra, plane geometry, trigonometry, and analytic geometry. Honors section available first semester.

132 Calculus II (R2) (both sem) 4 cr

The definite integral, techniques of integration, and applications to physics, chemistry, and engineering. Sequences, series, and power series. Taylor and MacLaurin series. Students expected to have and use a Texas Instruments 86 graphics, programmable calculator. Prerequisite: MATH 131 or equivalent. Honors section available.

135 Calculus I with Computer (R2) (1st sem) 4 cr

Calculus developed through its applications to population models, dynamical systems, optics, and physics. Techniques of differentiation of algebraic, trigonometric, exponential and logarithmic functions. Differential equations. Computers and MATHEMATICA software used to investigate ideas of calculus. No previous computer experience necessary. Prerequisite: high school algebra, plane geometry, trigonometry, and analytic geometry.

136 Calculus II with Computer (R2) (2nd sem) 4 cr

Continuation of MATH 135. Definition and applications of definite integral, techniques of integration, differential equations, infinite series, dynamical systems. Computers and MATHEMATICA software used to investigate ideas of calculus. Prerequisite: MATH 135.

233 Multivariate Calculus (R2) (both sem)

Techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals. Prerequisite: MATH 132, or 136. Students expected to have and use a Texas Instruments 86 graphics, programmable calculator. Honors section available.

235 Introduction to Linear Algebra (R2) (both sem)

Basic concepts of linear algebra. Matrices, determinants, systems of linear equations, vector spaces, linear transformations, and eigenvalues. Prerequisite or corequisite: MATH 132, or 136, or consent of instructor.

236 Linear Algebra with Computer Programming (R2) (2nd sem) 4 cr

Basic concepts of linear algebra. Enough of an array-oriented computer language such as APL, J, or MATHEMATICA to write programs that will solve systems of linear equations and related problems. Topics include those normally covered in MATH 235, with special effort to cover eigenvalues. Prerequisite or corequisite: MATH 132 or 136 or consent of instructor. No prior knowledge of computer programming assumed.

245 Multivariable Calculus, Linear Algebra, and Ordinary Differential Equations with Computer I
(1st sem) 4 cr

Unified treatment of the subjects in a context of real-world applications. Computers used to investigate concepts. Vector spaces and linear transformations; Markov chains; cross products and determinants; eigenvalues and eigenvectors; algebraic solution of ordinary differential equations. MATH 245 and 246 together are an alternative to MATH 233, 235, and 431. Prerequisites: MATH 135-136 or MATH 131-132.

246 Multivariable Calculus, Linear Algebra, and Ordinary Differential Equations with Computer II (2nd sem) 4 cr

Continuation of MATH 245. Vector methods for ordinary differential equations; multivariable derivatives; optimization; Fourier series and Fourier transform; line and surface integrals; multiple integrals, volume, and probability; introduction to partial differential equationsóall in a context of real-world applications. Computers used to investigate concepts. Prerequisite: MATH 245.

291 Seminar: Problem Solving (1st sem) 1 cr

A number of methods for solving problems; a wide variety of interesting and unusual problems. May be repeated for credit.

300 Fundamental Concepts of Mathematics (both sem)

Four to six topics, chosen from fields such as geometry, number theory, and the real numbers, with emphasis on precise def-initions, examples, conjectures, theorems, and proof methods, including induction and contradiction. Prerequisite: MATH 132 or 136 or consent of instructor.

331 Ordinary Differential Equations for Scientists and Engineers (both sem)

Introduction to ordinary differential equations. First and second order linear differential equations, systems of linear differential equations, Laplace transform, numerical methods, applications. Prerequisite: MATH 132, or 136; corequisite: MATH 233.

370 Writing in Mathematics (both sem)

Satisfies Junior Year Writing requirement. Develops research and writing skills in mathematics through peer review and revision. Students write on mathematical subject areas, prominent mathematicians, and famous mathematical problems. Prerequisites: MATH 300 and completion of College Writing (CW) requirement.

411 Introduction to Abstract Algebra I (both sem)

Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning. Prerequisites: MATH 235 or 236; MATH 300 or consent of instructor.

412 Introduction to Modern Algebra II (2nd sem)

Continuation of MATH 411. Prerequisite: MATH 411.

421 Complex Variables (both sem)

Complex numbers and functions, analytic functions, complex integration, series, residues, conformal mappings. Applications: computation of real integrals, Dirichlet's boundary value problem and its application to physics and engineering. Prerequisite: MATH 233.

425 Advanced Multivariate Calculus (both sem)

Calculus of several variables, Jacobians, implicit functions, inverse functions; multiple integrals, line and surface integrals, divergence theorem, Stokes' theorem. Prerequisites: MATH 233 and MATH 235 or 236.

455 Introduction to Discrete Structures (2nd sem)

Introduction to the wealth of pure mathematics and formal proofs. Discrete and continuous tools used to study discrete structures. Topics from algebraic coding theory, Boolean algebras, combinatorics, fields, finite state automata, graph theory, groups, number theory, and rings. Prerequisites: MATH 132 or 136, MATH 235/236 or CMPSCI 250.

456 Mathematical Modeling (R2) (2nd sem)

Introduction to the role of mathematics as a modeling tool. Construction and interpretation of mathematical models. Prerequisites: one year of calculus and consent of instructor. MATH 235 or 236 recommended as preparation.

461 Geometry I (1st sem)

Topics chosen from affine, projective, Euclidean, and non-Euclidean geometry. Highly recommended for prospective secondary school mathematics teachers. Prerequisite: MATH 235 or 236 and 300, or consent of instructor.

462 Geometry II (2nd sem)

A continuation of MATH 461. Prerequisite: MATH 461.

471 Number Theory

Basic properties of the positive integers including congruence arithmetic, the theory of prime numbers, quadratic reciprocity, and continued fractions. Theory applied to develop algorithms of computer science and to cryptography. Prerequisite: MATH 235 or 236.

475 History of Mathematics

History and development of mathematics from early Greeks to present day. Prerequisite: MATH 233.

491H, 492H Honors Seminar (both sem) 1 cr

Content varies from term to term and with instructor. What modern mathematics is all about; an appreciation of mathematics as part of our cultural heritage. Students solve specific problems and give class presentations. Outside speakers, films. When taken consecutively, 491H and 492H constitute one honors course.

503 Topics in Computer Connected Mathe-matics for Secondary Teachers (R2) (2nd sem)

Topics appropriate for secondary school mathematics courses using computers, focusing on algorithms, roundoff error, and graphics. Topics chosen from number theory, linear algebra, geometry, analysis, probability, and statistics. Prerequisites: MATH 233 and 235, plus working knowledge of some computer programming language.

511 Abstract Algebra I (1st sem)

Introduction to various topics in abstract algebra, such as groups, rings, and fields. A deeper and more advanced treatment than MATH 411. Prerequisites: MATH 235 or 236; MATH 300 or consent of instructor.

512 Abstract Algebra II (2nd sem)

A continuation of MATH 511.

523 Introduction to Modern Analysis (both sem)

Topics include intuitive set theory; equivalence relations; mathematical induction; integers and rational numbers; Dedekind completion; countability; sequences; topology of the reals and metric spaces; limits, continuity, differentiability, and integrability of functions. Prerequisites: MATH 233 and MATH 235 or 236; MATH 300 or consent of instructor.

532 Topics in Ordinary Differential Equations (1st sem)

Further methods for solving differential equations and qualitative methods for analyzing solutions of equations that cannot be solved explicitly. Topics: solution methods and basic theory of linear systems; stability and asymptotic behavior of linear and nonlinear systems, boundary value problems and Green's functions, Sturm-Liouville theory. Prerequisites: MATH 431 or 432 and MATH 235 or 236.

534 Introduction to Partial Differential Equations (2nd sem)

Introduction to solution methods for partial differential equations. Topics: classification and canonical forms, characteristics, separation of variables and Fourier series, maximum principles, the energy method, Green's functions, Fourier transforms. Prerequisites: MATH 233, MATH 235 or 236, and MATH 431 or 432.

545 Linear Algebra for Applied Mathematics (2nd sem)

Basic concepts: vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, Cayley-Hamilton Theorem. Inner product spaces and linear operators: orthogonal, unitary, self-adjoint, Hermitian. Diagonalization of symmetric matrices, applications. Topics in matrix theory. Prerequisite: MATH 235 or 236.

551 Introduction to Scientific Computing (1st sem)

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis. Prerequisites: MATH 233 and 235, or consent of instructor, and knowledge of a scientific programming language.

552 Applications of Scientific Computing (2nd sem)

Introduction to the application of computational methods to models arising in science and engineering, concentrating mainly on the solution of partial differential equations. Topics include finite differences, finite elements, boundary value problems, fast Fourier transforms. Prerequisite: MATH 551 or consent of instructor.

563 Introduction to Differential Geometry

Study of curves and surfaces in 3-dimensional Euclidean space which may be defined by smooth functions. The "extrinsic" geometry of curves and surfaces (how they sit in space); the intrinsic geometry of surfaces; properties of a surface that may be determined without reference to the ambient Euclidean space. Geodesics, fundamental forms, principal curvature, convex surfaces, Gauss-Bonnet Theorem. Prerequisites: MATH 233 and MATH 235 or 236, or consent of instructor.

Statistics

There is no undergraduate major in statistics. The curriculum is intended for those who wish to prepare for graduate work in statistics and for those who require statistics as a basic preparation for their own discipline.

111 Elementary Statistics (R2) (both sem)

Descriptive statistics, elements of probability theory, and basic ideas of statistical inference. Topics include frequency distributions, measures of central tendency and dispersion, commonly occurring distributions (binomial, normal, etc.), estimation, and testing of hypotheses. Prerequisite: high school algebra.

140 Introduction to Statistics (R2)
(both sem)

Basics of probability, random variables, binomial and normal distributions, central limit theorem, hypothesis testing, and simple linear regression.

501 Methods of Applied Statistics (R2) (both sem)

Statistical methods for research and experimental work, emphasizing practical issues; presentation of data, probability, sampling, hypothesis tests, parameter estimation, frequency data, regression, analysis of variance, design of experiments. Computer analysis of data (no computer experience necessary). A fast-paced course for students without extensive mathematical background. Prerequisite: high school algebra, Junior standing or higher.

505 Regression and Analysis of Variance (1st sem)

Applied statistics; including analysis of real data. Simple and multiple regression, including model fitting and selection, and diagnostics; one-way and n-way analysis of variance. Use of statistical packages (no computer experience necessary). Prerequisites: previous work in statistics, such as STATIS 501 or 516.

506 Design of Experiments (2nd sem)

Statistical considerations in planning, analysis, and interpretation of experiments; standard designs, e.g., factorials, block designs, Latin squares, and the associated analysis of variance; sample size determination; multiple comparisons; randomization; response surfaces. Computer analysis of data (no computer experience necessary). Prerequisite: previous work in statistics, such as STATIS 501 or 516.

511 Multivariate Statistical Methods

Introduction to the analysis of multivariate data. Topics include: description of multivariate data; random vectors; multivariate analysis of variance, repeated measures/profile analysis; and topics from multivariate regression, discriminant analysis, clustering, (principal components, factor analysis, and canonical correlation). Has a strong applied component involving the use of a statistical package for data analysis. Prerequisite: previous work in statistics such as STATIS 501 or 516; matrix theory helpful.

515 Statistics I (R2) (both sem)

First semester of a two-semester sequence. Emphasis given to probability theory necessary for application to and understanding of statistical inference. Probability models, sample spaces, conditional probability, independence. Random variables, expectation, variance, and various discrete and continuous probability distributions. Sampling distributions, the Central Limit Theorem and normal approximations. Multivariate calculus introduced as needed. Prerequisites: MATH 132, or 136.

516 Statistics II (R2) (2nd sem)

Basic theory of point and interval estimation and hypothesis testing; development in one and two sample problems, simple linear regression, and some topics out of one-way analysis of variance; discrete data and nonparametric methods. Prerequisite: STATIS 515.

Mathematics and Statistics | Courses | Faculty