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Index

Ithaca College Undergraduate Catalog 2002-2003

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    Mathematics Courses

313-10000 Mathematics Fundamentals   U LA

     Basic concepts underlying algebra, functions, exponents, areas, fractions, and percents. Reasoning skills required for these concepts. Word problems. Meets three hours. Prerequisites: Assignment based on math placement in Group 4. (See also 313-18000.) Credit cannot be earned for both 313-10000 and 313-18000. 1 credit. (F-S,Y)

313-10500 Mathematics for Decision Making   NS LA

     Introduction to probability theory; mathematics of finance; linear programming. Additional topics at the instructor's discretion. Students may not receive credit for both 313-10500 and 313-10600. Prerequisites: Math placement in Group 1, 2, or 3. 3 credits. (F-S,Y)

313-10600 Mathematics for Decision Making with Technology   NS LA 2b

     Introduction to probability theory; mathematics of finance; linear programming. Additional topics at the instructor's discretion. Appropriate technology is introduced to present some of the topics differently and in more depth than 313-10500. Students may not receive credit for both 313-10500 and 313-10600. Prerequisites: Math placement in Group 1, 2, or 3. 4 credits. (F-S,Y)

313-10700 Fundamentals of Applied Calculus   NS LA

    Introduction to calculus with an emphasis placed on problems in business and economics. Topics include modeling data with polynomial, exponential, and other functions; rates of change and other applications of derivatives; optimization; and the definite integral. Technology, such as graphing calculators, will be used throughout this course. Prerequisites: Math placement in Group 2 or 3. Completion of this course with a grade of C- or better will move students in Group 3 to Group 2. Not open to students who have taken 313-10800, 313-11100, or 313-11200. 4 credits. (F-S,Y)

313-10800 Calculus for Decision Making   NS LA 2b

     Introduction to calculus with an emphasis placed on problems in the social and life sciences. Topics include polynomial, exponential, and logarithmic functions and their derivatives; curve sketching, optimization, and rates of change; the definite integral and area. Further topics may be chosen from applications of differential equations and trigonometric functions. Prerequisites: Math placement in Group 1 or 2. Not open to students who have taken 313-10700, 313-10801, 313-10803, 313-11100, or 313-11200. Students with Group 1 placement who plan to take more than one semester of calculus should instead take 313-11100. 4 credits. (F-S,Y)

313-11100 Calculus I   NS LA 2b

    Calculus of functions of one variable. Topics include limits, continuity, derivatives, applications of derivatives (problems of motion, graphing, and optimization), antiderivatives, and an introduction to the definite integral. Functions covered include polynomial, rational, exponential, logarithmic, trigonometric, and piecewise-defined functions. Prerequisites: Math placement in Group 1. 4 credits. (F-S,Y)

313-11200 Calculus II   NS LA 2b

    Continuation of calculus of functions of one variable. Topics include differential equations, including slope fields, numerical solutions, and separation of variables; evaluation of integrals and antiderivatives; applications of integration; improper integrals; series, with an emphasis placed on power series. Prerequisites: 313-11100. 4 credits. (F-S,Y)

313-13100 Power Algebra   NS LA 2b

    College algebra is introduced as motivated by applications. Students make conjectures and predictions about real-life applications and actively participate in constructing simple mathematical models. Focus on mathematical concepts and thinking rather than algebraic manipulations. Provides the skills and knowledge to take a course such as Calculus for Decision Making. Upon the recommendation of the instructor, students completing this course move to Group 2. Students not receiving the recommendation of the instructor have the option of taking the department exam to move from Group 3 to 2. Students may not receive credit for 313-10100 and 313-13100. Prerequisites: Math placement in Group 3. 4 credits. (F-S,Y)

313-13200 Dynamic Functions   NS LA 2b

    Using a blend of geometric, numerical, and symbolic approaches, students construct mathematical models to better understand a variety of real-life applications. A graphical and analytic analysis specifically focuses on exponential, logarithmic, and trigonometric function theory, motivated by practical problems. Explores and develops precalculus mathematics while focusing on mathematics as a practical tool. Upon the recommendation of the instructor, students completing this course move to Group 1 in placement. Students not receiving the recommendation of the instructor have the option of taking the department placement exam to move from Group 2 to Group 1. Students may not receive credit for both 313-10200 and 313-13200. Prerequisites: Math placement in Group 2. 4 credits. (F-S,Y)

313-13500 Mathematical Art with Computers   LA 2b

    Focuses on mathematical concepts such as symmetry, crystallographic groups, recursive patterns, spirals, and the golden ratio as they relate to geometric design. The use of computers enables us to explore these topics without an extensive math background. Prerequisites: Math placement in Group 3, 2, or 1. 3 credits. (S,Y)

313-14400 Business Statistics   NS LA

    Descriptive statistical techniques; introduction to probability; statistical inference including problems of estimation and hypothesis testing; correlation and regression analysis. Technology used in this course may include graphing calculators and statistical software. Prerequisites: Math placement in Group 1 or 2. A student cannot receive credit for this course and 670-39000. Not open to students who have completed 313-24300, 313-24400, 313-24402, or 313-31600. To obtain mathematical maturity, it is strongly recommended that a student complete a calculus course before taking this course. 4 credits. (F-S,Y)

313-15200 Selected Topics: What Is Mathematics?   NS LA 2b

    Cultural approach to selected topics in mathematics. See instructor for current list of topics. Students may not receive credit for both 313-15200 and 313-25200. Prerequisites: Math placement in Group 3, 2, or 1. 3 credits. (F-S,Y)

313-15500 Basic Statistical Reasoning   NS LA 2b

    Basic concepts involved in statistical reasoning, such as sampling and experimental design, description of data, normal approximation to data, correlation and regression, and probability. Emphasis is placed on understanding the use of statistics rather than on how to do statistical analysis. Prerequisites: Math placement in Group 3, 2, or 1; completion of one course in the social or natural sciences. Not open to students who have taken 313-10800, 313-11100, 330-20700, or 670-39000. 3 credits. (F-S,Y)

313-16100 Math and Society   NS LA 2b

    Explores connections between mathematics and the liberal arts. Covers three to six topics chosen for their mathematical and societal component, with comparable emphasis given to each component. Only a high school math background is assumed, but students must have scored in Group 2 or 1 on the Math Placement Exam. Actual course content varies with instructor, but examples of topics are exponential growth and world population; symmetry and group theory in art and architecture; fair allocation and equity; binomial models and the death penalty; quantitative communication and the media. Prerequisites: Math placement in Group 2 or 1. 3 credits. (F-S,Y)

313-17600 Mathematical Problem Solving with Technology   NS LA

    Topics include procedural programming: loops, conditionals, procedures, and recursion. These concepts are used in mathematical contexts and applications that involve both problem solving and the use of technology. The application of Gaussian elimination to solving systems of linear equations is one of these applications. Introduces a computer algebra system and a procedural programming language. Use of spreadsheets and programmable graphing calculators may be included. Prerequisites or corequisites: 313-11100. 4 credits. (S,Y)

313-18000 Mathematics Fundamentals with Computers   U LA

     Meets four hours. Three of the four hours explore the same topics as 313-10000 Mathematics Fundamentals: reasoning skills and basic concepts underlying algebra, functions, exponents, areas, fractions, and percents. The fourth hour is a computer lab, where students use the computer to increase their understanding of mathematics. Prerequisites: Math placement in Group 4. Credit cannot be earned for both 313-18000 and 313-10000. 2 credits. (F-S,Y)

313-19000 Selected Topics in Mathematics   NS LA

     Topics to be determined by instructor and department. May be repeated for credit for selected topics on different subjects. Prerequisites: Appropriate to topics. 1-4 credits. (IRR)

313-19200 Independent Study   U LA

     Reading on selected subjects with frequent, informal discussions with the instructor. Prerequisites: Permission of instructor. 1-3 credits. (IRR)

313-21100 Calculus III   NS LA 2b

     Introduction to vectors and the geometry of vector spaces. Calculus of functions of several variables: partial derivatives, gradients, optimization, double integrals. Prerequisites: 313-1110 0; 313-11200. 4 credits. (F-S,Y)

313-21200 Calculus IV   NS LA

     Multiple integrals and change of variables. Line and surface integrals. Classical theorems of vector calculus. Prerequisites: 313-21100. 3 credits. (S,Y)

313-24300 Statistics   NS LA

     Descriptive statistical techniques; review of basic probability; random variables and their distributions; statistical inference including problems of estimation and hypothesis testing; and correlation and regression analysis. Prerequisites: Either 313-10500 or 313-10600 and math placement in Group 2; or 313-11100 and 313-11200. A student cannot receive credit for this course and 670-39000 or 313-24400. Not open to students who have taken 313-31600. 3 credits. (F-S,Y)

313-24400 Statistics with Probability   NS LA 2b

    Descriptive statistical techniques; introduction to probability theory including counting methods, expected value, independence, and random variables and their distributions; statistical inference including problems of estimation and hypothesis testing; correlation and regression analysis; introduction to further topics chosen from Chi-square tests, multiple regression, and analysis of variance. Technology used in this course may include graphing calculators and statistical software. Prerequisites: 313-10800 or 313-11100. A student cannot receive credit for this course and 670-39000, 313-14400, 313-24300, or 313-24402. Not open to students who have taken 313-31600. 4 credits. (F-S,Y)

313-25000 Problem-Solving Seminar   NS LA

     Techniques used in the solution of diverse mathematical problems are developed and discussed. The problems are drawn from areas such as geometry and calculus. Prerequisites: 313-26000. 1 credit. (F,Y)

313-25200 Selected Topics: What Is Mathematics?   NS LA 2b

    Cultural approach to selected topics in mathematics. See instructor for current list of topics. Prerequisites: Math placement in Group 2; one college mathematics course or sophomore standing. Students may not receive credit for both 313-15200 and 313-25200. 3 credits. (F,Y)

313-26000 Linear Algebra, Modeling, and Reasoning I   NS LA

    A study of mathematical reasoning including standard methods of proof, such as direct proof, indirect proof, proof by cases, and use of the contrapositive, induction, and quantification. Functions, matrices, and matrix algebra, eigenvalues, and characteristic polynomials are studied theoretically and used to provide tools in applications. Other topics, such as set theory, may be included. Tools developed may include transformation matrices, coding matrices, and incidence matrices. Prerequisites or corequisites: 313-11200. 4 credits. (F,Y)

313-26100 Linear Algebra, Modeling, and Reasoning II   NS LA

    Topics include equivalence relations, abstract linear algebra: abstract vector spaces, independence, bases, dimension, and linear maps. Analytic, numeric, and geometric solutions of first order differential equations are studied. Topics in modeling such as solutions of constant coefficient second order differential equations, homogeneous and non-homogeneous differential equations, discrete dynamical systems, difference equations, and graph theory. Prerequisites: 313-26000. 4 credits. (S,Y)

313-28000 Mathematica   U LA

     Introduction to Mathematica -- its syntax, structure, and distinctive features. Use of Mathematica as a problem-solving tool for mathematics. Prerequisites: 313-11200. 1 credit. (F,Y)

313-29000 Selected Topics in Mathematics   NS LA

     Topics to be determined by instructor and department. This course may be repeated for credit for selected topics on different subjects. Prerequisites: As appropriate to topics. 1-4 credits. (IRR)

313-29100 Sophomore Seminar   NS LA

     Series of discussions presenting an overview of mathematics led by various faculty members. Given on a pass/fail basis only. Should be taken by majors in sophomore year. Prerequisites: 313-11100; 313-11200; 313-26000 as a prerequisite or corequisite. 1 credit. (S,Y)

313-29200 Independent Study   U LA

     Readings on selected subjects with frequent, informal discussions with the instructor. Prerequisites: Permission of instructor. 1-3 credits. (IRR)

313-30300 Abstract Algebra   NS LA

     Introduction to algebraic structures. Study includes concepts from group theory, ring theory, or field theory. Topics may include Abelian groups, cyclic groups, permutation groups, factor groups, ideals, quotient rings, integral domains, isomorphisms, and homomorphisms. Additional topics may be included. Prerequisites: 313-26100. 4 credits. (F,Y)

313-30500 Introduction to Analysis   NS LA

     Topology of the real line. Continuity, differentiability, and integrability of functions of a real variable. Prerequisites: 313-21100; 313-26100. 4 credits. (S,Y)

313-31600 Probability/Statistics   NS LA

    Specific content varies. Topics may include some of the following: probability systems; random variables, their distributions and expected values; Poisson and the theory of Markov processes; estimation theory (point, interval, and Bayesian inference); hypothesis testing; regression theory; correlation; and time series. Prerequisites: 313-21100; 313-26100. 4 credits. (F,O)

313-34000 Operations Research   NS LA

    Emphasis is placed on mathematics used in applications. Specific content varies. Topics may include some of the following: mathematical modeling such as linear programming, dynamic programming, applied Markov processes, queuing theory, and game theory; numerical analysis, such as numerical solutions of linear and nonlinear equations, interpolation, numerical differentiation and integration, numerical solutions to differential equations, and functional approximations; simulation such as Monte Carlo methods, continuous models, discrete events, random number generation, and statistical output analysis; applied graph theory; applied statistics; and applied dynamical systems. Prerequisites: 313-21100; 313-26100. 4 credits. (S,O)

313-36200 Modern Geometry   NS LA

     Rigorous development of Euclidean and hyperbolic geometry from both a metric and synthetic point of view. Some topics in transformational geometry are also covered. Prerequisites: 313-26100; one course at the level of 313-21200 or higher, excluding 313-26000. 4 credits. (F,E)

313-39000 Selected Topics in Mathematics   NS LA

     Topics to be determined by instructors and department. Fulfills a required mathematics elective. This course may be repeated for credit for selected topics on different subjects. Prerequisites: 313-26100, or equivalent, and as appropriate to topics. 1-4 credits. (IRR)

313-39100 Independent Study   U LA

     Reading on selected subjects with frequent, informal discussions with the instructor. This course may be repeated for credit for different studies. Does not fulfill a required mathematics elective. Prerequisites: 313-26100, or equivalent. 1-3 credits. (IRR)

313-39200 Independent Study   U LA

     Reading on selected subjects with frequent, informal discussions with the instructor. Fulfills a required mathematics elective. This course may be repeated for credit for different studies. Prerequisites: 313-26100, or equivalent. 1-3 credits. (IRR)

313-39500 Selected Topics in Mathematics   NS LA

     Topics to be determined by instructors and department. This course may be repeated for credit for selected topics on different subjects. Does not fulfill a required mathematics elective. Prerequisites: 313-26100, or equivalent, and as appropriate to topics. 1-4 credits. (F-S,Y)

313-39700 Junior Seminar   NS LA

    Students will work with faculty on focused mathematical investigations. Research problems will be presented by faculty teaching Research Experience in Mathematics (313-39810). Students will attend a variety of talks related to mathematics. Weekly problem solving related to research topics. Given on a pass/fail basis only. Prerequisites: 313-29100. 1 credit. (F, Y)

313-39800 Mathematical Explorations   NS LA

    An active research experience in mathematics. Students may produce original research, devise new proofs of known results, or experience a guided discovery of known results. Topics vary. Prerequisites: 313-26100; permission of instructor. May be repeated for degree credit but can only be counted once toward major requirements. 4 credits. (F,Y)

313-39810 Research Experience in Mathematics   NS LA

    Students actively participate in mathematical investigation and exposition, working collaboratively on research questions. Review of relevant literature and research methods will be incorporated. Students are required to present their findings both in writing (consistent with the standards of the discipline) and in public presentations. Topics vary by instructor. Prerequisites: 313-39700; permission of instructor. 3 credits (S,Y)

313-40100 Theoretical Continuous Mathematics   NS LA

    Emphasis is on mathematical topics in which the concept of continuity plays a key role. Specific content varies. Topics may include, but are not limited to, some of the following: topology such as point-set topology, metric topology, geometric topology, differential topology, and manifold theory; advanced real analysis, such as sequences and series of functions, convergence of functions, integration theory; topology of the real line, function theory; complex analysis such as analytic functions, conformal mappings, elementary functions and power series, complex integration and calculus of residues; advanced differential equations, such as ordinary equations of first and higher orders, singular solutions, total differential equations, and solution by series; fractal geometry; and continuous dynamical systems. Prerequisites: At least one level-3 mathematics course; permission of the instructor. 4 credits. (S,E)

313-40200 Theoretical Discrete Mathematics   NS LA

    Emphasis is placed on mathematical topics principally concerned with discrete entities. Specific content varies. Topics may include, but are not limited to, some of the following: number theory, such as properties of integers, diophantine equations, congruence, and quadratic reciprocity; algebra, such as advanced topics in group, ring, and field theory, automorphisms, and Galois theory; graph theory; discrete dynamical systems; and combinatorics. Prerequisites: 313-30300. 4 credits. (S,O)

313-48000 Connections in Advanced Mathematics   NS LA

    Study of connections and relationships among various disciplines within mathematics. Specific content varies. Topics may include, but are not limited to, some of the following: a historical development of mathematics and various philosophies of mathematics; cultural similarities and differences in viewpoints and developments in mathematics; cross-discipline approaches that combine sub-disciplines such as probability techniques in number theory and random graph theory; field theory and geometric constructions; and algebraic topology. Prerequisites: At least one level-3 course in mathematics or the related discipline; permission of instructor. 4 credits. (S,E)

313-49000 Selected Topics in Advanced Mathematics   NS LA

     Topics to be selected by instructor and students. Fulfills a required mathematics elective. This course may be repeated for credit for selected topics on different subjects. Prerequisites: 313-26100, or equivalent, and as appropriate to topics. 3 credits. (IRR)

313-49100 Independent Study   U LA

     Reading on selected advanced subjects, with frequent, informal discussions with the instructor. Does not fulfill a required mathematics elective. This course may be repeated for credit for different studies. Prerequisites: Permission of instructor. 1-3 credits.

313-49200 Independent Study   U LA

     Reading on selected advanced subjects, with frequent, informal discussions with the instructor. Fulfills a required mathematics elective. This course may be repeated for credit for different studies. Prerequisites: Permission of instructor. 1-3 credits.

313-49300-313-49400 Honors Course   NS LA

     Preparation of honors thesis in partial fulfillment of requirement for graduation with honors in mathematics. Prerequisites: Honors standing in mathematics. 1-2 credits. (IRR)

313-49500 Selected Topics in Advanced Mathematics   NS LA

     Topics to be selected by instructor and students. This course may be repeated for credit for selected topics on different subjects. Does not fulfill a required mathematics elective. Prerequisites: 313-26100, or equivalent, and as appropriate to topics. 3 credits.

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