**MATH 10000 - Mathematics Fundamentals LA**

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 2B LA NS**

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. 3 credits. (F-S,Y)

**MATH 10600 - Mathematics for Decision Making with Technology 2B LA NS**

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. 4 credits. (F-S,Y)

**MATH 10700 - Fundamentals of Applied Calculus LA NS**

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- or 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. 4 credits. (F-S,Y)

**MATH 10800 - Calculus for Decision Making 2B LA NS**

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 10801, MATH 10803, 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. 4 credits. (F-S,Y)

**MATH 11100 - Calculus I 2B LA NS**

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)

**MATH 11200 - Calculus II 2B LA NS**

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 2B LA NS**

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. Students may not receive credit for both MATH 10100 and MATH 13100. Prerequisites: Math placement in group 3. 4 credits. (F-S,Y)

**MATH 13200 - Dynamic Functions 2B LA NS**

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 placement in group 1. 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 MATH 10200 and MATH 13200. Prerequisites: Math placement in group 2. 4 credits. (F-S,Y)

**MATH 13500 - Mathematical Art with Computers 2B LA NS**

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 3, 2, or 1. 3 credits. (S,Y)

**MATH 14400 - Business Statistics LA NS**

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. A student cannot receive credit for this course and PTBS39000, MATH 24300, MATH 24400. Not open to students who have completed MATH 21600. To attain mathematical maturity, students are strongly encouraged to complete a calculus course before taking this course. Prerequisites: Math placement in group 1 or 2. 4 credits. (F-S,Y)

**MATH 15200 - Selected Topics: What Is Mathematics? 2B LA NS**

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 3, 2, or 1. 3 credits. (F-S,Y)

**MATH 15500 - Basic Statistical Reasoning 2B LA NS**

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 3, 2, or 1; completion of one course in the social or natural sciences. 3 credits. (F-S,Y)

**MATH 16100 - Math and Society 2B LA NS**

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)

**MATH 18000 - Mathematics Fundamentals with Computers LA**

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 LA NS**

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. 3 credits. (S,Y)

**MATH 19000 - Selected Topics in Mathematics 2B LA NS**

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 LA**

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

**MATH 21100 - Calculus III 2B LA NS**

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 LA NS**

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 LA NS**

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 LA NS**

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

**MATH 23100 - Linear Algebra LA NS**

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 24300 - Statistics LA NS**

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. A student cannot receive credit for this course and PTBS 39000, MATH 14400 or MATH 24400. Not open to students who have taken MATH 21600. Prerequisites: MATH 10500 or MATH 10600 and math placement in group 2, or MATH 11200.

3 credits. (F-S,Y)

**MATH 24400 - Statistics with Probability 2B LA NS**

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. A student cannot receive credit for this course and PTBS 39000, MATH 14400, or MATH 24300. Not open to students who have taken MATH 21600. Prerequisites: MATH 10800 or MATH 11100. 4 credits. (F-S,Y)

**MATH 25000 - Problem-Solving Seminar LA NS**

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 25200 - Selected Topics: What Is Mathematics? 2B LA NS**

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 2; one college mathematics course or sophomore standing. 3 credits. (F,Y)

**MATH 27000 - Mathematical Reasoning with Discrete Mathematics LA NS**

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 concurrentlyl. 3 credits. (S,Y)

**MATH 28000 - Mathematica LA**

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 LA NS**

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 LA NS**

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 23100 or MATH 27000 (MATH 27000 may be taken concurrently). Pass/fail only. 1 credit. (S,Y)

**MATH 29200 - Independent Study: Math LA**

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

**MATH 30300 - Abstract Algebra LA NS**

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 LA NS**

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/Statistics LA NS**

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 LA NS**

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 LA NS**

Topics to be determined by instructors 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 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: MATH 27000. 1-3 credits. (IRR)

**MATH 39200 - Independent Study: Mathematics 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: MATH 27000. 1-3 credits. (IRR)

**MATH 39700 - Junior Seminar LA NS**

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 LA NS**

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 LA NS**

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 LA NS**

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 LA NS**

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 LA NS**

Topics in graph theory include basic properties of graphs, Eulerian trails, Hamilton chains, trees, and may include the chromatic ploynomial, planar graphs, and the independence number. Topics in comninatories 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 LA NS**

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 LA NS**

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 LA NS**

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 LA NS**

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 26100 or equivalent; other prerequisites as appropriate to topics. 3 credits. (IRR)

**MATH 49200 - Independent Study: Mathematics LA NS**

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 LA NS**

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 LA NS**

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