# MATH - Mathematics

## MATH 10000 Mathematics Fundamentals

Basic concepts underlying algebra, functions, exponents, areas, fractions, and percents. Reasoning skills required for these concepts. Word problems. Meets three hours. See also MATH 18000; credit cannot be earned for both MATH 10000 and MATH 18000. Prerequisites: Math placement in group 4. 1 credit. (F-S,Y)

## MATH 10500 Mathematics for Decision Making

Introduction to probability theory, mathematics of finance and linear programming. Additional topics at the instructor's discretion. Students may not receive credit for both MATH 10500 and MATH 10600. Prerequisites: Math placement in group 1, 2, or 3, or completion of MATH 10000 or MATH 18000 with a grade of C- or better. 3 credits. (F-S,Y)

## MATH 10600 Mathematics for Decision Making with Technology

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 MATH 10500. Students may not receive credit for both MATH 10500 and MATH 10600. Prerequisites: Math placement in group 1, 2, or 3, or completion of MATH 10000 or MATH 18000 with a grade of C- or better. 4 credits. (F-S,Y)

## MATH 10700 Fundamentals of Applied Calculus

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. Completion of this course with a grade of C- ot better will move students in group 3 to group 2. Not open to students who have taken MATH 10800, MATH 11100, or MATH 11200. Prerequisites: Math placement in group 2 or 3, or completion of MATH 10000 or MATH 18000 with a grade of C- or better. 4 credits. (F-S,Y)

## MATH 10800 Calculus for Decision Making

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. Not open to students who have taken MATH 10700, MATH 11100, or MATH 11200. Students with group 1 placement who plan to take more than one semester of calculus should instead take MATH 11100. Prerequisites: Math placement in group 1 or 2, or completion of MATH 13100 with a grade of C- or better. 4 credits. (F-S,Y)

## MATH 11000 College Algebra and Trigonometry

A modeling approach to college algebra and trigonometry. Topics include algebraic expressions (including radicals and exponents); equations and inequalities; polynomial and rational functions; exponential and logarithmic functions; systems of equations; trigonometric functions and properties. Prerequisites: Math Placement 2 or 3. 4 credits. (F-S,Y)

## MATH 11100 Calculus I

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, or completion of MATH 11000 with a grade of C- or better. 4 credits. (F-S,Y)

## MATH 11200 Calculus II

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: MATH 11100. 4 credits. (F-S,Y)

## MATH 13100 Power Algebra

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 MATH 10800 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. Prerequisites: Math placement in group 3. 4 credits. (F-S,Y)

## MATH 13500 Mathematical Art with Computers

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 students to explore these topics without an extensive math background. Prerequisites: Math placement in group 1, 2, or 3, or completion of MATH 10000 or MATH 18000 with a grade of C- or better. 3 credits. (S,Y)

## MATH 14400 Statistics for Business, Economics and Management

A first course in statistics covering descriptive statistical techniques; introduction to probability; statistical inference including problems of estimation and hypothesis testing; correlation and regression analysis; and multiple regression. Data sets and exercises will be chosen from the fields of business, economics, and management. Technology used in this course may include graphing calculators and statistical software. Prerequisite: Math placement in group 1 or 2, or completion of MATH 10700 or MATH 13100 with a grade of C- or better. A student cannot receive credit for this course and PTBS 39000. Not open to students who have completed MATH 14500 or MATH 21600. 4 credits (F-S, Y)

## MATH 14500 Statistics for the Health, Life, and Social Sciences

A first course in statistics covering descriptive statistical techniques; introduction to probability; statistical inference including problems of estimation and hypothesis testing; one-way ANOVA; and design of experiments. Most of the data sets and exercises will be chosen from the fields of biology, health, and life sciences, as well as from everyday life. Technology used in this course may include graphing calculators and statistical software. Prerequisite: Math placement group 1 or 2, or completion of MATH 10700 or MATH 13100 with a grade of C- or better. A student cannot receive credit for this course and PTBS 39000. Not open to students who have completed MATH 14400 or MATH 21600. 4 credits. (F-S, Y)

## MATH 15200 Selected Topics: What Is Mathematics?

Cultural approach to selected topics in mathematics. See instructor for current list of topics. Students may not receive credit for both MATH 15200 and MATH 25200. Prerequisites: Math placement in group 1, 2, or 3, or completion of MATH 10000 or MATH 18000 with a grade of C- or better. 3 credits. (F-S,Y)

## MATH 15500 Basic Statistical Reasoning

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. Not open to students who have taken MATH 10800, MATH 11100, PSYC 20700, or PTBS 39000. Prerequisites: Math placement in group 1, 2, or 3, or completion of MATH 10000 or MATH 18000 with a grade of C- or better; completion of one course in the social or natural sciences. 3 credits. (F-S,Y)

## MATH 16100 Math and Society

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 1 or 2, or completion of MATH 13100 with a grade of C- or better. 3 credits. (F-S,Y)

## MATH 18000 Mathematics Fundamentals with Computers

Meets four hours. Three of the four hours explore the same topics as MATH 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. Credit cannot be earned for both MATH 18000 and MATH 10000. Prerequisites: Math placement in group 4. 2 credits. (F-S,Y)

## MATH 18500 Math Experimentation

Students explore mathematical phenomena experimentally, detect patterns, and provide mathematical explanations for these patterns. Students gain insight into mathematical thinking and the process of conjecture by designing and implementing mathematical algorithms with a Computer Algebra System. Discrete dynamical systems including Markov chains will be investigated. Other topics vary but may include the distribution of prime numbers, modular arithmetic, the Collatz Conjecture. Prerequisites: Math placement in group 1, or completion of MATH 11000 with a grade of C- or better. 3 credits. (S,Y)

## MATH 19000 Selected Topics in Mathematics

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)

## MATH 19200 Independent Study: Math

Individual study of selected subjects extending the student's mathematical knowledge. Prerequisites: Permission of instructor. 1-3 credits. (IRR)

## MATH 21100 Calculus III

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

## MATH 21200 Calculus IV

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

## MATH 21400 Differential Equations

Topics will include modeling with differential equations, existence and uniqueness of solutions, separation of variables; first order linear equations; second order equations with constant coefficients; homogeneous equations, phase plane analysis, eigenvalues; and systems of differential equations. Additional topics may include: series solutions of differential equations, non-linearity and equilibrium analysis, and transforms among others. Prerequisites: MATH 11200. 3 credits. (S,Y)

## MATH 21600 Introduction to Mathematical Statistics

An introduction to statistical analysis for students with a calculus background. Topics will include statistical modeling, probability theory and distributions, parameter estimation, hypothesis testing, linear regression, and experimental design. Statistical literacy and techniques for data analysis will be emphasized. Prerequisites: MATH 11200. 3 credits. (F,Y)

## MATH 22000 Mathematics for Childhood Education

This is a math content course for future elementary school teachers. Students develop a deep understanding of mathematical content, strengthen their mathematical reasoning and problem-solving skills, and learn how to help elementary students make mathematical sense of their world. Prerequisite: EDUC 21910 or EDUC 34000 (may be taken concurrently.) 3 credits. (S,Y)

## MATH 23100 Linear Algebra

Topics include systems of linear equations and solutions; matrix operations; linear independence, span, basis, dimension, rank; linear operators and matrix representations; vector spaces, subspaces, change of coordinates; eigenvalues, eigenvectors; and applications. Prerequisites: MATH 11200. 3 credits. (F,Y)

## MATH 25000 Problem-Solving Seminar

Techniques used in the solution of diverse mathematical problems are developed and discussed. Problems will often be drawn from national competitions, such as the Putnam exam and the COMAP Modeling Competition, or from problem sections of mathematics journals. The course will be offered for either 0.5 or 1 credit ; it may be repeated for credit up to a total of 4 credits. Prerequisites: MATH 11100. Pass/fail only. 0.5-1 credit. (F,S)

## MATH 27000 Mathematical Reasoning with Discrete Mathematics

Focus is on the underpinnings of and strategies for mathematical arguments that constitute mathematical proof. These underpinnings include logical connectives, (universal and existential) quantification, and rules of deductive inference. Strategies include direct proof, indirect proof, "proof" by counterexample, proof by cases, and proof by induction. Students learn to employ these strategies and concepts to create basic mathematical proofs. Content topics include, but are not limited to, fundamentals concepts of sets and functions as well as multiple topics from discrete mathematics that include elementary counting principles. Prerequisites: MATH 23100 or MATH 18500. MATH 18500 may be taken concurrently. 3 credits. (S,Y)

## MATH 28000 Mathematica

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

## MATH 29000 Selected Topics in Mathematics

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

## MATH 29100 Sophomore Seminar

Series of discussions presenting an overview of mathematics led by various faculty members. Should be taken by majors in sophomore year. Prerequisites: MATH 11200; MATH 18500 or MATH 23100. Pass/fail only. 1 credit. (S,Y)

## MATH 29200 Independent Study: Math

Individual study of selected subjects extending the student's mathematical knowledge. Prerequisites: Permission of instructor. 1-3 credits. (IRR)

## MATH 30300 Abstract Algebra

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: MATH 27000. 4 credits. (F,Y)

## MATH 30500 Introduction to Analysis

Topology of the real line. Continuity, differentiability, and integrability of functions of a real variable. Prerequisites: MATH 21100; MATH 27000. 4 credits. (S,Y)

## MATH 31600 Probability

Topics include probability systems; random variables, their distributions, and expected values. Additional topics may include queueing theory, the theory of Poisson processes and the theory of Markov processes. Prerequisites: MATH 21100. 3 credits. (S,Y)

## MATH 36200 Modern Geometry

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: MATH 27000. 4 credits. (F,Y)

## MATH 39000 Selected Topics in Mathematics

Topics to be determined byinstructors and department. Fulfills a required mathematics elective. This course may be repeated for credit when topics vary. Prerequisites: MATH 27000. 1-4 credits. (IRR)

## MATH 39100 Independent Study: Mathematics

Individual study of selected subjects extending the student's mathematical knowledge. This course may be repeated for credit for different studies. Does not fulfill a required mathematics elective. Prerequisites: MATH 27000. 1-3 credits. (IRR)

## MATH 39200 Independent Study: Mathematics

Individual study of selected subjects extending the student's mathematical knowledge. Fulfills a required mathematics elective. This course may be repeated for credit for different studies. Prerequisites: MATH 27000. 1-3 credits. (IRR)

## MATH 39700 Junior Seminar

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

## MATH 39810 Research Experience in Mathematics

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: MATH 39700; permission of instructor. 3 credits. (S,Y)

## MATH 41000 Selected Topics in Continuous Mathematics

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, topology, manifold theory, fractal geometry, advanced real analysis, differential topology, advanced differential equations, and continuous dynamical systems. Prerequisites: MATH 27000; at least one level-3 mathematics course. 3 credits. (IRR)

## MATH 41100 Complex Analysis

Students explore the theory of functions defined in the complex plane, highlighting the interplay between geometric visualization and analysis. Topics include the geometry of analytic mappings, power series, Cauchy's Theorem, and the Residue Theorem. Connections to other areas of mathematics and to other scientific fields will be explored through applications. Prerequisites: MATH 27000; at least one level-3 mathematics course. 3 credits. (IRR)

## MATH 42000 Selected Topics in Discrete Mathematics

Emphasis is placed on mathematical topics principally concerned with discrete entities. Specific content varies. Topics include, but are not limited to, number theory, fair division, game theory, discrete dynamical systems and advanced topics in group, ring, or field theory. Prerequisites: MATH 27000; at least one level-3 mathematics course. 3 credits. (IRR)

## MATH 42100 Graph Theory and Combinatorics

Topics in graph theory include basic properties of graphs, Eulerian trails, Hamilton chains, trees, and may include the chromatic polynomial, planar graphs, and the independence number. Topics in combinatorics include the pigeonhole principle, permutations and combinations, the binomial theorem, and may include generating functions, Catalan numbers, and Stirling numbers. Prerequisites: MATH 27000; at least one level-3 mathematics course. 3 credits. (IRR)

## MATH 43000 Selected Topics in Applied Mathematics

Emphasis is on mathematics topics in an applied setting. Topics may include, but are not limited to mathematical modeling, partial differential equations, wavelets, scheduling theory, applied dynamical systems, and actuarial mathematics. Prerequisites: MATH 27000; at least one level-3 mathematics course. 3 credits. (IRR)

## MATH 43100 Numerical Analysis

Theory and applications of numerical techniques. Topics will include error analysis, solution of non-linear equations and systems of equations, interpolation, approximation, numerical integration and differentiation and numerical solution of initial-value problems. Prerequisites: MATH 27000 and at least one level-3 mathematics course. 3 credits. (IRR)

## MATH 48000 Connections in Advanced Mathematics

Study of connections and relationships among various disciplines within mathematics. Specific content varies. Topics may include, but are not limited to, the following: historical development of mathematics and various philosophies of mathematics, cultural similarities and differences in viewpoints and developments in mathematics, cross-discipline approaches that combine subdisciplines such as probability techniques in number theory and random graph theory, field theory and geometric constructions, and algebraic topology. Prerequisites: MATH 27000 and at least one level-3 course in mathematics or the related discipline; permission of instructor. 3 credits. (S,E)

## MATH 49000 Selected Topics in Advanced Mathematics

Topics to be selected by instructor and students. Fulfills a required mathematics elective. This course may be repeated for credit when topics vary. Prerequisites: MATH 27000 or equivalent; other prerequisites as appropriate to topics. 3 credits. (IRR)

## MATH 49200 Independent Study: Mathematics

Individual study of selected subjects extending the student's mathematical knowledge. Fulfills a required mathematics elective. This course may be repeated for credit. Prerequisites: Permission of instructor. 1-3 credits.

## MATH 49201 Independent Study: Math

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

## MATH 49300 Honors Course: Math

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

## MATH 49400 Honors Course: Math

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

## MATH 49800 Capstone in Mathematics I

Students reflect on the field of mathematics via an integrative project developed in concert with a faculty mentor. Students analyze mathematical ideas related to their projects and integrate this knowledge with ideas learned in the mathematics curriculum. Students begin work on a comprehensive thesis that they will complete in MATH 49900. Prerequisites: Senior standing; MATH 30300 or 30500; additional 3 credits in mathematics at level 3 or 4. 3 credits. (F,Y)

## MATH 49900 Capstone in Mathematics II

Students reflect upon the field of mathematics via an integrative project developed in concert with a faculty mentor. Students analyze mathematical ideas related to their projects and integrate this knowledge with ideas learned in the mathematics curriculum. Students complete a comprehensive thesis (begun in MATH 49800) and give a public presentation. Prerequisites: MATH 49800. 1 credit. (S, Y)