313-10000 Mathematics-Fundamentals U LA
Understanding 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)
313-10100 Intermediate Algebra U LA
Topics include exponents; factoring; algebra of polynomials and rational expressions; linear, quadratic, polynomial, and rational functions; logarithmic and exponential functions. Meets four hours. This course is intended primarily as preparation for 313-10800 Calculus for Decision Making. Students may not receive credit for 313-10100 and 313-13100. Prerequisites: Math placement in Group 3. 2 credits. (F-S,Y)
313-10200 Precalculus U LA
Topics include a review of algebra; functions; exponential, logarithmic, and trigonometric functions; analytic geometry. Meets four hours. This course is intended primarily as preparation for 313-11100 Calculus I. Students may not receive credit for 313-10200 and 313-13200. Prerequisites: Math placement in Group 2. 3 credits. (F-S,Y)
313-10500 Mathematics for Decision Making NS LA
Introduction to probability theory; mathematics of finance; introduction to 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; introduction to 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)
313-10800 Calculus for Decision Making NS LA
An introduction to calculus with emphasis on problems in business, economics, and social science. Topics include polynomial, exponential, and logarithmic functions and their derivatives; curve sketching, optimization, and rates of change; the definite integral and area. Prerequisites: Math placement in Group 1 or 2. Not open to students who have taken 313-11100 or 313-11200. 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 emphasis 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. The focus is on mathematical concepts and thinking rather than algebraic manipulations. This course 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 Group 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. Students explore and develop 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
This course 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)
313-15200 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. (S,Y)
313-15300 Writing Seminar in Mathematics NS LA
For freshmen who want to read, think, learn, and write about mathematics, with emphasis on the last. Weekly writing assignments based on reading and/or class discussion of mathematics. Individual consultation on writing problems. Topics include elementary group theory, projective geometry, number theory, and cardinality of sets. 4 credits. (IRR)
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 on understanding the use of statistics rather than on how to do statistical analysis. Prerequisites: Math placement in Group 3, 2, or 1; and completion of one course in the social or natural sciences. Not open to students who have taken 313-10800, 313-11100, 330-20700, 331-10300, 640-29000, or 670-39000. 3 credits. (F-S,Y)
313-16100 Math and Society NS LA 2b
The course explores some unexpected connections between mathematics and the liberal arts. It 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 course topics include 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: Group 2 or 1 on math placement test. 3 credits. (F-S,Y)
313-17600 Mathematical Problem Solving with Technology NS LA
Topics include procedural programming: loops, recursion, conditionals and flow of control, and procedures. 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. Techniques and platforms introduced include the use of a computer algebra system and a procedural programming language. In addition, use of spreadsheets, and programmable graphing calculators may be included. Prerequisite or Co-requisite: 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. This course may be repeated for credit for selected topics on different subjects. Prerequisites: As 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 per semester. (IRR)
313-21100 Calculus III NS LA
Introduction to vectors and the geometry of vector spaces. Calculus of functions of several variables: partial derivatives, gradients, optimization, double integrals. Prerequisites: 313-11100 and 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)
313-21500 Mathematics of Discrete Structures NS LA
Mathematical treatment of some of the discrete, finite structures used in computer science, mathematics, and applied mathematics. Topics include graph theory, elementary combinatorics and discrete probability, Boolean algebra and circuit design, and finite automata and regular grammars. Selected topics such as predicate logic, coding theory, lattice theory, and other types of grammars and automata. Prerequisites: 313-26100 and 312-17100. 4 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 313-31400. 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, random variables and their distributions; statistical inference including problems of estimation and hypothesis testing; correlation and regression analysis. Prerequisites: 313-10800 or 313-11100. A student cannot receive credit for this course and, 670-39000, or 313-24300. Not open to students who have taken 313-31400. 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 and either 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. Prerequisite or corequisite: 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. Prerequisite: 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 and 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 per semester. (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 and 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 and 313-26100. 4 credits. (F,O)
313-34000 Operations Research NS LA
Emphasis is 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 and 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 and 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 per semester. (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 per semester. (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)
313-39800 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 and permission of instructor. May be repeated for degree credit but can only be counted once toward major requirements. 4 credits. (F,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: 313-30500. 4 credits. (S,E)
313-402000 Theoretical Discrete Mathematics NS LA
Emphasis is 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 mathematics course at level 3 and permission of the 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 per semester.
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 per semester.
313-49300-49400 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 per semester. (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.
