This course is supplemental instruction that is required for 92.111, Quantitative Reasoning. Students will meet one hour per week with the instructor for additional tutelage. The credits in this course can not be used to satisfy the credits required for graduation, but may be used to satisfy the credits required for full time student status.
Co-Requisite: 92.111 Quantitative Reasoning
An introduction to the mathematics concepts and skills important in modern society, even for non-technical pursuits. The course will emphasize conceptual understanding as well as a facility in performing elementary computations. Topics to be examined will include types of reasoning, problem-solving methods, techniques of estimation, algebraic essentials, and the nature of probability and statistics.
No credit in Science or Engineering.
Review of algebra: operations on the real numbers, factoring, radical notation, and rational exponents. Linear and quadratic equations, rational expressions. Graphs of functions, straight lines, parabolas, exponential and log functions, systems of equations, and linear mathematical models.
Prerequisites: No credit for math/science/engineering majors.
Differential calculus: limits, continuity, derivatives, differentials, higher-order derivatives, implicit differentiation, maxima and minima of functions, and applications of derivatives to business and economics. Integrals and Applications to business.
No credit in Science or Engineering.
Pre-Req: 92.121 Management Precalculus
Reviews angles and their measure, the trigonometric functions, solving triangles, law of sines, law of cosines, circular functions and their graphs, vectors and trigonometric identities.
Pre-Req: 92.121 Management Precalculus
Serves as a first course in calculus and provides a brief review of analytic geometry and trigonometric functions. The course progresses to the study of inverse functions, limits, continuity, derivatives, rules for differentiation of algebraic and transcendental functions, chain rule, implicit differentiation, linear approximation, differentials, and maximum and minimum values.
Pre-Req: 92.123 Precalculus Math II
Serves as a continuation of 92.125. The course covers LHopitals Rule, optimization problems, Newtons method, sigma notation, integration, area between curves, volume, arc length, surface area, integration by parts, trigonometric substitution, partial fraction decomposition, and improper integrals.
Pre-Req: 92.125 Calculus A
A review of precalculus (algebra and trigonometry) together with development of problem solving skills. No credit for math/science/engineering majors.
Serves as a first course in calculus. Functions, limits, continuity, derivatives, rules for differentiation of algebraic and transcendental function; chain rule, implicit differentiation, related rate problems, max/min problems, and curve sketching. Integrals and areas.
Serves as a continuation of Calculus I. Volume, arc length, surface area, pressure and force. Differentiation and integration of trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions. Improper integration, infinite series, Taylor and MacLauren series.
Pre-Req: 92.131 Calculus I with a C or better
This course covers the same topics as 92.131 Calculus I, but in an enriched environment.
This course covers the same topics as 92.132 Caluculus II, but in an enriched environment.
An introduction to the nature of mathematics, providing insights into what mathematics is, what it accomplishes, and how it is pursued as a human enterprise. The course will stress concepts and relevance to modern experience, with topics to be selected at the discretion of each instructor from a wide variety of interesting and illustrative fields of mathematics.
No credit in Science or Engineering.
NOTE: This course is no longer offered under this course number. The course is now offered under 92.283 Introduction to Statistics.
An investigation of creative mathematics through the lives of mathematicians from classical times to the present.
Elementary set theory and solution sets of systems of linear equations. An introduction to proofs and the axiomatic methods through a study of the vector space axioms. Linear analytic geometry. Linear dependence and independence, subspaces, basis. Inner products. Matrix algebra. Applications of the above will also be discussed.
Pre-Req: 92.132 Calculus II
Linear transformations. Linear operators, change of basis, inner product and the diagonalization problem. Quadratic forms. Convex sets and geometric programming, input/output models for an economy, Markov chains, other applications of linear algebra.
Pre-Req: 92.221 Linear Algebra I
Serves as a continuation of 92.126. This course covers integration by parts, integration of trigonometric integrals, trigonometric substitution, partial fraction, numeric integration, improper integrals, L'Hopital's Rule, indeterminate forms, sequences, infinite series, integral tests, comparison tests, alternating series tests, power series, Taylor series, polar coordinates, graphs and areas in polar coordinates, and parametric equations.
Serves as a continuation of 92.225. This course covers curvature, cylindrical surfaces, dot and cross products, curves and planes in three space, cylindrical and spherical coordinates, functions of two variables, chain rule, directional derivatives and gradient, tangent planes, and double and triple integrals in rectangular, polar, cylindrical and spherical coordinate systems.
Serves as a continuation of Calculus II Polar Coordinates, parametric equations, vectors and analytic geometry in space. Functions of several variables, partial derivatives, and chain rule. Tangent planes and normal lines. Maxima and minima, Lagrange multipliers, and multiple integrals.
Pre-Req: 92.132 Calculus II with 'C' or better
An introduction to mathematics related software. Topics from Calculus & Differential Equations will be explored using a symbolic package like Maple. the course will also introduce LaTeX, the standard for typesetting mathematics.
Classification and solution of ordinary differential equations of the first order and higher orders. The Laplace transform. Applications .
Pre-Req: 92.132 Calculus II
Introduction to differential equations with an emphasis on engineering applications. Topics include first-order equations, higher-order linear equations with constant coefficients, and systems of first-order equations. Applications of each topic are introduced and qualitative, analytical, and numerical solution techniques are studied. Laplace transform methods are discussed. The software package MATLAB may be used throughout the course.
Pre-Req: 92.132 Calculus II
Covers the same topics as 92.231 Calculus II, but in an enriched environment.
An introduction to descriptive statistics, graphing and data analysis, probability laws, discrete and continuous probability distributions, correlation and regression, inferential statistics.
No credit for Math, Science, or Engineering majors.
Not for Mathematics Majors
Discusses vector analysis, Green's Theorem, Divergence Theorem, Stokes' Theorem, Fourier series, integrals, and partial differential equations of physics and engineering.
Pre-Req: 92.231 Calculus III and 92.234 Differential Equations or 92.236 Eng Differential Equations
Introduces students to matrix algebra, solution of systems of linear equations, eigenvalues and eigenvectors, solution of differential equations by matrix methods, series solution of differential equations, Bessel and Legendre functions, and Sturm-Liouville problems.
Pre-Req: 92.231 Calculus III and 92.234 Differential Equations or 92.236 Eng Differential Equations
Presents real and complex number systems. Sequences and series of complex numbers. Theory of metric spaces: completeness, compactness, continuity, uniform continuity. Differentiability of functions, and Taylor's Theorem.
Pre-Req: 92.221 Linear Algebra I and 92.231 Calculus III
Probability, random variables, discrete and continuous densities, expectation and variance, special distributions (binomial, Poisson, normal, gamma, etc.), moment generating functions, joint and conditional distributions, transformations of variables, sampling, central limit theorem.
Point estimation and confidence intervals, hypothesis testing, correlation, linear regression, analysis of variance for the one- and two-way design, nonparametric methods, chi-square tests for contingency tables.
A two-part learning course. The first half of the semester takes place in the classroom with students working on a methematics project. The function of the project is to learn some mathematics and serve as a model for how to approach a research project. In the second half of the semester, with the course instructor as mentor, students work with grade 6-12 students in a local school to develop a project for their school mathematics fairs. As a final product, students will submit a two-part report consisting of a poster presentation of their own project and a diary of experiences in mentoring the math fair projects.
Presents propositional logic, combinatorics, methods of proof, mathematical systems, algebra of sets, matrix algebra, relations and functions, recursion and generating functions, applications to computer science, and graph theory.
Pre-Req: 92.131 Calculus I
Examines graph theory, trees, algebraic systems, Boolean algebra, groups, monoids, automata, machines, rings and fields, applications to coding theory, logic design, and sorting.
Pre-Req: 92.321 Discrete Structures I
This course is an introduction to symbolic logic. Symbolic logic provides a solid foundation in formal reasoning for students preparing for further study in mathematics, linguistics,cognitive science, computer science or philosophy. Topics include propositional logic, first-order logic and systems of deduction. Tarski's notion of model, and the completeness and incompleteness theorems of Godel. Prerequisite: 92.321.
Pre-Req: 92.131 Calculus I
Basic concepts of data. Linear lists, strings, arrays, and orthogonal lists. Trees and graphs. Storage systems and structures. Storage allocation and collection. Multilinked structures. Symbol tables, searching and sorting (ordering) techniques.
Pre-Req: 92.231 Calculus III
Focuses on the theory and application of numerical techniques including error analysis. Also discusses solution of linear, nonlinear and differential equations, interpolation, numerical integration, and curve fitting. Computer solutions are emphasized.
Pre-Req: 92.231 Calculus III and 92.234 Differential Equations or 92.236 Eng Differential Equations)
Computer analysis of data derived from research conducted in physical, social, and life sciences. Data preparation. Data modification, file manipulation, and descriptive statistics using SPSS. Programming ability is not required.
No credit in Science or Engineering.
Pre-Requisite: 92.283 Introduction to Statistics or equivalent
Student works with an advisor to develop a proposal for a senior project that will be carried out as part of 92.475 Senior Seminar II. Generally taken during the spring of the junior year. Prerequisite: permission of instructor.
Introduction to experimental design, data analysis and formal statistical procedures from an applied point of view.
Pre-Req: 92.132 Calculus II
Provides a one-semester course in probability and statistics with applications in the engineering sciences. Probability of events, discrete and continuous random variables cumulative distribution, moment generatory functions, chi-square distribution, density functions, distributions. Introduction to estimation, hypothesis testing, regression and correlation.
Pre-Req: 92.132 Calculus II
Development of number systems, including axiomatic and constructive treatment of the integers and the reals; sequences and series; functions of a real variable and their properties, including continuity, derivatives and integrals; functions of several real variables, including partial derivatives and multiple integration; differential equations and applications; metric spaces.
Addresses the topics of probability, random variables, discrete and continuous densities, expectation and variance, special distributions (binomial, Poisson, normal, etc.), moment generating functions, joint and conditional distributions, transformations of variables, sampling, and the central limit theorem.
Discusses point estimation and confidence intervals, sufficiency, efficiency, Fisher's Lemma, Cramer-Rao bound, hypothesis testing, correlation, linear regression, analysis of variance for the one- and two-way design, non parametric methods, chi-square tests for contingency tables.
Discusses complex numbers, functions of a complex variable, mappings, derivatives, analytic functions, elementary functions. Laurent series, residues and poles, contour integration.
Pre-Req: 92.231 Calculus III
Studies congruencies and the Chinese Remainder Theorem, Primitive roots, quadratic reciprocity, approximation properties of continued fractions, Pell's equation. Recent application of number theory such as primality testing, cryptology, and random number generation will also be covered.
Pre-Req: 92.221 Linear Algebra I or 92.321 Discrete Structures I
A project -based course starting with an introduction to the basic features of Mathematica. A project that allows the student to focus on certain features in more detail is required and occupies the second half of the course.
Focuses on: mathematical resources, ability to use heuristics, the student's beliefs about the use of mathematics to solve problems, and the student's self-confidence as a problem solver. Effective strategies for incorporating problem solving in the curriculum will also be discussed.
Pre-Req: 92.221 Linear Algebra I or 92.321 Discrete Structures I
Elementary group theory, groups, cosets, normal subgroups, quotient groups, isomorphisms, homomorphisms, applications.
Pre-Req: 92.221 Linear Algebra I
Discusses elementary rings and field theory, quotient rings and ideals, homomorphism of rings, rings of polynomials, algebraic extensions, automorphisms of fields, separable extensions, and the Galois Theory.
Pre-Req: 92.421 Algebraic Structures
Metric spaces, topological spaces, connectedness, compactness, the fundamental group, classifications of surfaces, Brouwer's fixed point theorem.
Pre-Req: 92.305 Intro to Real Analysis I
Provides a wide survey of topics related to secondary school geometry; axiomatic systems and Euclidean geometry; constructions in geometry; analytic geometry; and introduction to Noneuclidean geometry.
Pre-Req: 92.221 Linear Algebra I or 92.321 Discrete Structures I
Examines ancient numeral systems, Babylonian and Egyptian mathematics, Pythagorean mathematics, duplication, trisection, and quadrature, Euclid's Elements and Greek mathematics after Euclid, Hindu and Arabian mathematics, European mathematics from 500 to 1600, origins of modern mathematics, analytic geometry, the history of calculus. Also covers the transition to the twentieth century and contemporary perspectives.
Pre-Req: 92.132 Calculus II
Pre-Req: 92.234 Differential Equations or 92.236 Eng Differential Equations
Representation of Signals: Fourier analysis, fast Fourier transforms, orthogonal expansions. Transformation of signals: linear filters, modulation. Band-limited signals. Sampling. Uncertainty principle. Windows and extrapolation. Applications to medical imaging and array processing.
Pre-Req: 92.231 Calculus III and 92.234 Differential Equations or 92.236 Eng Differential Equations
Applications of mathematics to real life problems. Topics include dimensional analysis, population dynamics wave and heat propagation, traffic flow.
Pre-Req: 92.132 Calculus II
Undergraduate seminar on advanced mathematical topics. Students are required to develop an understanding of an advanced subject beyond the scope of an existing course or synthesize two or more different areas form their curriculum. Students are required to participate in the seminar, present their results to the Department and write a substantial thesis in their topic area. Essential course elements include library research, original research, and both verbal and written exposition. The first semester is a graduation requirement for majors in mathematics.
Pre-Req: 92.375 or 92.474 Senior Seminar I
An optional second semester seminar to allow for continuation of study initiated in Senior Seminar I.
Pre-Req: 92.475 Senior Seminar II
Point estimation, confidence intervals, hypothesis testing. Two-sample t-test. Correlation and linear regression. The bivariate normal distribution. Analysis of variance for one-and two-way designs. F tests. Nonparametric methods. Chi-squared tests for contingency tables. Generalized likelihood ratio. C.R. bound. Consistency. Prerequisite: 92.386.
Pre-Req: 92.386 Prob & Stats I
Individual study for the student desiring more advanced or more specialized work .
Course may not be substituted for scheduled offerings.
Prerequisite: Permission of Department Chair
Individual study for the student desiring more advanced or more specialized work in algebra. May be repeated for a total of six semester credits. Course may not be substituted for scheduled offerings.
Individual study for the student desiring more advanced or more specialized work in analysis. May be repeated for a total of six semester credits. Course may not be substituted for scheduled offerings.
Individual study for the student desiring more advanced or more specialized work in geometry. May be repeated for a total of six semester credits. Course may not be substituted for scheduled offerings.
Individual study for the student desiring more advanced or more specialized work in Statistics. May be repeated for a total of six semester credits. Course may not be substituted for scheduled offerings. Prerequisite: Permission of Department Chair.
