Undergraduate Bulletin - Illinois Institute of Technology
Undergraduate Bulletin - Illinois Institute of Technology Undergraduate Bulletin - Illinois Institute of Technology
Course Descriptions LIT 380 Topics in Literature An investigation into a topic of current or enduring interest in literature, which will be announced by the instructor when the course is scheduled. Prerequisite(s): [(HUM 102) OR (HUM 104) OR (HUM 106)] (3-0-3) (C)(H) LIT 411 Workshop in Creative Writing A workshop demonstrating principles of composition in fiction, poetry, or drama, studied from a writer’s vantage point. Works by modern authors are analyzed. Student manuscripts are discussed and evaluated. Prerequisite(s): [(HUM 102) OR (HUM 104) OR (HUM 106)] (3-0-3) (C)(H) LIT 491 Independent Reading & Research Consent of department. For advanced students. Prerequisite(s): [(HUM 102) OR (HUM 104) OR (HUM 106)] (Credit: Variable) (C)(H) Mathematics Courses indicated by an asterisk (*) do not count toward any computer science, engineering, mathematics, or natural science degree program. MATH 100 Introduction to the Profession Introduces the student to the scope of mathematics as a profession, develops a sense of mathematical curiosity and problem solving skills, identifies and reinforces the student’s career choices, and provides a mechanism for regular academic advising. Provides integration with other first-year courses. Introduces applications of mathematics to areas such as engineering, physics, computer science, and finance. Emphasis is placed on the development of teamwork skills. (3-0-3) (C) MATH 119* Geometry for Architects Basic analytic geometry in two and three dimensions; trigonometry. Equations of lines, circles and conic sections; resolution of triangles; polar coordinates. Equations of planes, lines, quadratic surfaces. Applications. (3-0-3) (C) MATH 122* Introduction to Calculus Basic concepts of calculus of a single variable; limits, derivatives, integrals. Applications. (3-0-3) MATH 130* Thinking Mathematically This course allows students to discover, explore, and apply modern mathematical ideas. Emphasis is placed on using sound reasoning skills, visualizing mathematical concepts, and communicating mathematical ideas effectively. Classroom discussion and group work on challenging problems are central to the course. Topics from probability, statistics, logic, number theory, graph theory, combinatorics, chaos theory, the concept of infinity, and geometry may be included. (3-0-3) (C) MATH 148* Calculus/Precalculus I Review of algebra and analytic geometry. Functions, limits, derivatives. Trigonometry, trigonometric functions and their derivatives. Chain rule, implicit and inverse functions, and inverse trigonometric functions. (4-0-4) MATH 149 Calculus/Precalculus II Applications of derivatives; related rates, maxima and minima, monotonicity, concavity, graphing, optimization. Antiderivatives, first order differential equations. Definite integral and applications. Implicit and inverse functions, and inverse trigonometric functions. Prerequisite(s): [(MATH 148 with min. grade of C)] (4-1-5) (C) MATH 151 Calculus I Analytic geometry. Functions and their graphs. Limits and continuity. Derivatives of algebraic, trigonometric and inverse trigonometric functions. Applications of the derivative. Introduction to integrals and their applications. Prerequisite(s): [(IIT Mathematics Placement: 151) OR (MATH 148 with min. grade of C)] (4-1-5) (C) MATH 152 Calculus II Transcendental functions and their calculus. Integration techniques. Applications of the integral. Indeterminate forms and improper integrals. Polar coordinates. Numerical series and power series expansions. Prerequisite(s): [(MATH 149 with min. grade of C) OR (MATH 151 with min. grade of C)] (4-1-5) (C) MATH 230 Introduction to Discrete Math Sets, statements, and elementary symbolic logic; relations and digraphs; functions and sequences; mathematical induction; basic counting techniques and recurrence. Credit will not be granted for both CS 330 and MATH 230. (3-0-3) (C) MATH 251 Multivariate & Vector Calculus Analytic geometry in three-dimensional space. Partial derivatives. Multiple integrals. Vector analysis. Applications. Prerequisite(s): [(MATH 152)] (4-0-4) MATH 252 Introduction to Differential Equations Linear differential equations of order one. Linear differential equations of higher order. Series solutions of linear DE. Laplace transforms and their use in solving linear DE. Introduction to matrices. Systems of linear differential equations. Prerequisite(s): [(MATH 152)] (4-0-4) MATH 300 Perspectives in Analysis The course is focused on selected topics related to fundamental concepts and methods of classic analysis and their applications with emphasis on various problem-solving strategies, visualization, mathematical modeling, and interrelation of different areas of mathematics. Prerequisite(s): [(MATH 251 and MATH 252)] (3-0-3) MATH 332 Elementary Linear Algebra Systems of linear equations; matrix algebra, inverses, determinants, eigenvalues, and eigenvectors, diagonalization; vector spaces, basis, dimension, rank and nullity; inner product spaces, orthonormal bases; quadratic forms. Prerequisite(s): [(MATH 251*)] An asterisk (*) designates a course which may be taken concurrently. (3-0-3) 234
Course Descriptions MATH 333 Matrix Algebra & Complex Variables Vectors and matrices; matrix operations, transpose, rank, inverse; determinants; solution of linear systems; eigenvalues and eigenvectors. The complex plane; analytic functions; contour integrals; Laurent series expansions; singularities and residues. Course does not satisfy graduation requirements for Applied Mathematics majors. Prerequisite(s): [(MATH 251)] (3-0-3) MATH 350 Introduction to Computational Mathematics Study and design of mathematical models for the numerical solution of scientific problems. This includes numerical methods for the solution on linear and nonlinear systems, basic data fitting problems, and ordinary differential equations. Robustness, accuracy, and speed of convergence of algorithms will be investigated including the basics of computer arithmetic and round-off errors. Same as MMAE 350. Prerequisite(s): [(CS 104) OR (CS 105) OR (CS 115)] AND [(MATH 251)] AND [(MATH 252)] (3-0-3) (C) MATH 400 Real Analysis Real numbers, continuous functions; differentiation and Riemann integration. Functions defined by series. Prerequisite(s): [(MATH 251)] (3-0-3) MATH 402 Complex Analysis Analytic functions, conformal mapping, contour integration, series expansions, singularities and residues, and applications. Intended as a first course in the subject for students in the physical sciences and engineering. Prerequisite(s): [(MATH 251)] (3-0-3) MATH 405 Introduction to Iteration & Chaos Functional iteration and orbits, periodic points and Sharkovsky’s cycle theorem, chaos and dynamical systems of dimensions one and two. Julia sets and fractals, physical implications. Prerequisite(s): [(MATH 251, MATH 252, and MATH 332) OR (MATH 251, MATH 252, and MATH 333)] (3-0-3) (C) MATH 410 Number Theory Divisibility, congruencies, distribution of prime numbers, functions of number theory, diophantine equations, applications to encryption methods. Prerequisite(s): [(MATH 230)] (3-0-3) MATH 420 Geometry The course is focused on selected topics related to fundamental concepts and methods of Euclidean geometry in two and three dimensions and their applications with emphasis on various problem-solving strategies, geometric proof, visualization, and interrelation of different areas of mathematics. Prerequisite: Permission of instructor. (3-0-3) MATH 425 Statistical Methods Concepts and methods of gathering, describing and analyzing data including basic statistical reasoning, basic probability, sampling, hypothesis testing, confidence intervals, correlation, regression, forecasting, and nonparametric statistics. No knowledge of calculus is assumed. This course is useful for students in education or the social sciences. This course does not count for graduation in any mathematics programs. Credit not given for both MATH 425 and MATH 476. Course does not satisfy graduation requirements for Applied Mathematics majors. (3-0-3) MATH 426 Statistical Tools for Engineers Descriptive statistics and graphs, probability distributions, random sampling, independence, significance tests, design of experiments, regression, time-series analysis, statistical process control, introduction to multivariate analysis. Same as CHE 426. Credit not given for both Math 426 and CHE 426 Course does not satisfy graduation requirements for Applied Mathematics majors. Requires sophomore standing. (3-0-3) MATH 430 Applied Algebra Relations; modular arithmetic; group theory: symmetry, permutation, cyclic, and abelian groups; group structure: subgroups, cosets, homomorphisms, classifications theorems; rings and fields. Applications to crystallography, cryptography, and check-digit schemes. Prerequisite(s): [(MATH 230) OR (MATH 332)] (3-0-3) (C) MATH 431 Applied Algebra II Ring homomorphisms; factorization and reducibility in polynomial rings; integral domains; vector spaces; fields and their extensions. As time permits, application to one or more of the following: Frieze and crystallographic groups, Caley digraphs, and coding theory. Prerequisite(s): [(MATH 430)] (3-0-3) MATH 435 Linear Optimization Introduction to both theoretical and algorithmic aspects of linear optimization: geometry of linear programs, simplex method, anticycling, duality theory and dual simplex method, sensitivity analysis, large scale optimization via Dantzig- Wolfe decomposition and Benders decomposition, interior point methods, network flow problems, integer programming. Credit may not be granted for both MATH 435 and MATH 535. Prerequisite(s): [(MATH 332)] (3-0-3) MATH 453 Combinatorics Permutations and combinations; pigeonhole principle; inclusion-exclusion principle; recurrence relations and generating functions; enumeration under group action. Prerequisite(s): [(MATH 230)] (3-0-3) 235
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Course Descriptions<br />
LIT 380<br />
Topics in Literature<br />
An investigation into a topic <strong>of</strong> current or enduring interest<br />
in literature, which will be announced by the instructor when<br />
the course is scheduled.<br />
Prerequisite(s): [(HUM 102) OR (HUM 104) OR (HUM 106)]<br />
(3-0-3) (C)(H)<br />
LIT 411<br />
Workshop in Creative Writing<br />
A workshop demonstrating principles <strong>of</strong> composition in<br />
fiction, poetry, or drama, studied from a writer’s vantage<br />
point. Works by modern authors are analyzed. Student<br />
manuscripts are discussed and evaluated.<br />
Prerequisite(s): [(HUM 102) OR (HUM 104) OR (HUM 106)]<br />
(3-0-3) (C)(H)<br />
LIT 491<br />
Independent Reading & Research<br />
Consent <strong>of</strong> department. For advanced students.<br />
Prerequisite(s): [(HUM 102) OR (HUM 104) OR (HUM 106)]<br />
(Credit: Variable) (C)(H)<br />
Mathematics<br />
Courses indicated by an asterisk (*) do not count toward any<br />
computer science, engineering, mathematics, or natural science<br />
degree program.<br />
MATH 100<br />
Introduction to the Pr<strong>of</strong>ession<br />
Introduces the student to the scope <strong>of</strong> mathematics as a<br />
pr<strong>of</strong>ession, develops a sense <strong>of</strong> mathematical curiosity and<br />
problem solving skills, identifies and reinforces the student’s<br />
career choices, and provides a mechanism for regular academic<br />
advising. Provides integration with other first-year<br />
courses. Introduces applications <strong>of</strong> mathematics to areas<br />
such as engineering, physics, computer science, and finance.<br />
Emphasis is placed on the development <strong>of</strong> teamwork skills.<br />
(3-0-3) (C)<br />
MATH 119*<br />
Geometry for Architects<br />
Basic analytic geometry in two and three dimensions;<br />
trigonometry. Equations <strong>of</strong> lines, circles and conic sections;<br />
resolution <strong>of</strong> triangles; polar coordinates. Equations <strong>of</strong><br />
planes, lines, quadratic surfaces. Applications.<br />
(3-0-3) (C)<br />
MATH 122*<br />
Introduction to Calculus<br />
Basic concepts <strong>of</strong> calculus <strong>of</strong> a single variable; limits, derivatives,<br />
integrals. Applications.<br />
(3-0-3)<br />
MATH 130*<br />
Thinking Mathematically<br />
This course allows students to discover, explore, and apply<br />
modern mathematical ideas. Emphasis is placed on using<br />
sound reasoning skills, visualizing mathematical concepts,<br />
and communicating mathematical ideas effectively. Classroom<br />
discussion and group work on challenging problems<br />
are central to the course. Topics from probability, statistics,<br />
logic, number theory, graph theory, combinatorics, chaos<br />
theory, the concept <strong>of</strong> infinity, and geometry may be included.<br />
(3-0-3) (C)<br />
MATH 148*<br />
Calculus/Precalculus I<br />
Review <strong>of</strong> algebra and analytic geometry. Functions, limits,<br />
derivatives. Trigonometry, trigonometric functions and their<br />
derivatives. Chain rule, implicit and inverse functions, and<br />
inverse trigonometric functions.<br />
(4-0-4)<br />
MATH 149<br />
Calculus/Precalculus II<br />
Applications <strong>of</strong> derivatives; related rates, maxima and<br />
minima, monotonicity, concavity, graphing, optimization.<br />
Antiderivatives, first order differential equations. Definite<br />
integral and applications. Implicit and inverse functions, and<br />
inverse trigonometric functions.<br />
Prerequisite(s): [(MATH 148 with min. grade <strong>of</strong> C)]<br />
(4-1-5) (C)<br />
MATH 151<br />
Calculus I<br />
Analytic geometry. Functions and their graphs. Limits and<br />
continuity. Derivatives <strong>of</strong> algebraic, trigonometric and inverse<br />
trigonometric functions. Applications <strong>of</strong> the derivative.<br />
Introduction to integrals and their applications.<br />
Prerequisite(s): [(IIT Mathematics Placement: 151) OR<br />
(MATH 148 with min. grade <strong>of</strong> C)]<br />
(4-1-5) (C)<br />
MATH 152<br />
Calculus II<br />
Transcendental functions and their calculus. Integration<br />
techniques. Applications <strong>of</strong> the integral. Indeterminate forms<br />
and improper integrals. Polar coordinates. Numerical series<br />
and power series expansions.<br />
Prerequisite(s): [(MATH 149 with min. grade <strong>of</strong> C) OR<br />
(MATH 151 with min. grade <strong>of</strong> C)]<br />
(4-1-5) (C)<br />
MATH 230<br />
Introduction to Discrete Math<br />
Sets, statements, and elementary symbolic logic; relations and<br />
digraphs; functions and sequences; mathematical induction;<br />
basic counting techniques and recurrence. Credit will not be<br />
granted for both CS 330 and MATH 230.<br />
(3-0-3) (C)<br />
MATH 251<br />
Multivariate & Vector Calculus<br />
Analytic geometry in three-dimensional space. Partial<br />
derivatives. Multiple integrals. Vector analysis. Applications.<br />
Prerequisite(s): [(MATH 152)]<br />
(4-0-4)<br />
MATH 252<br />
Introduction to Differential Equations<br />
Linear differential equations <strong>of</strong> order one. Linear differential<br />
equations <strong>of</strong> higher order. Series solutions <strong>of</strong> linear DE.<br />
Laplace transforms and their use in solving linear DE. Introduction<br />
to matrices. Systems <strong>of</strong> linear differential equations.<br />
Prerequisite(s): [(MATH 152)]<br />
(4-0-4)<br />
MATH 300<br />
Perspectives in Analysis<br />
The course is focused on selected topics related to fundamental<br />
concepts and methods <strong>of</strong> classic analysis and their<br />
applications with emphasis on various problem-solving strategies,<br />
visualization, mathematical modeling, and interrelation<br />
<strong>of</strong> different areas <strong>of</strong> mathematics.<br />
Prerequisite(s): [(MATH 251 and MATH 252)]<br />
(3-0-3)<br />
MATH 332<br />
Elementary Linear Algebra<br />
Systems <strong>of</strong> linear equations; matrix algebra, inverses, determinants,<br />
eigenvalues, and eigenvectors, diagonalization; vector<br />
spaces, basis, dimension, rank and nullity; inner product<br />
spaces, orthonormal bases; quadratic forms.<br />
Prerequisite(s): [(MATH 251*)] An asterisk (*) designates a<br />
course which may be taken concurrently.<br />
(3-0-3)<br />
234