2011-2012 University Catalog archived
Mathematics (MATH)
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(Society of the Cincinnati Foundation)
Professors Bourdon, Dresden, Dymàček, Feldman, Evans, McRae
Distinguished Visiting Professor Humke
Assistant Professors Crowley, Finch, Siehler
Visiting Assistant Professor Choi
HONORS: An Honors Program in mathematics is offered for well-qualified majors; see department head for details.
Military Engineering—For qualified students who may request it, a course in fortifications, gunnery, and ballistics will be offered.
Major
Minor
MATH 101 - Calculus I
FDR: FM
Credits: 3
Planned Offering: Fall, Winter
An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem.
Topics for Fall 2011:
MATH 101A (3) — Calculus I. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. This class is for students who have already taken Calculus and meets four days a week. (FM)
MATH 101B (3) — Calculus I: A First Course. Students who have already taken Calculus may not take this course. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. This class is restricted to and specially tailored for those who are beginning their study of calculus. This class meets four days per week. (FM) Bourdon
MATH 101D (3) — Calculus I: Calculus Explorations. If you throw a ball up, which is greater, its ascent time or descent time? How long does it take to drain a tank? Can your bank compound interest continuously? Is there any chaos in calculus? How well does a tangent line really approximate a graph? What are the three pillars of calculus and how are they used? Through exploration of a variety of applications, this course will reinforce your calculus skills, while introducing you to some useful new ideas and techniques for problem solving. This class is for students who have already taken Calculus and meets three days a week. (FM) Feldman
Math 101E (3) — Calculus & Environmental Issues. An introduction to the calculus of functions of one variable, including a study of limits, derivatives, extrema, integrals, and the fundamental theorem. In addition, this course will have an applied component centered on sustainability. Using data about natural resources (e.g., coal, water) and pollutants (e.g., carbon dioxide emissions), students will find mathematical models appropriate for the data, and then use the models and calculus to make predictions about pollution levels and the availability of resources given our current consumption. This class is for students who have already taken Calculus and meets three days a week. (FM) Finch
Math 101H (3) — Calculus I: Calculus and Its Historical Development. This course is designed for liberal-arts students, emphasizing the historical and philosophical development of ideas at the root of calculus and the nature of mathematics. As grammar, rhetoric, and logic played an important role in the classical liberal-arts education, this course involves intensive writing. (FM) McRae
MATH 102 - Calculus II
FDR: SC
Credits: 3
Planned Offering: Fall, Winter
Prerequisite: The equivalent of MATH 101 with C grade or better. A continuation of MATH 101, including techniques and applications of integration, transcendental functions, and infinite series. Staff.
MATH 118 - Introduction to Statistics
FDR: SC
Credits: 3
Planned Offering: Winter
Prerequisite: MATH 101. Elementary probability and counting. Mean and variance of discrete and continuous random variables. Central Limit Theorem. Confidence intervals and hypothesis tests concerning parameters of one or two normal populations.
MATH 121 - Discrete Mathematics I
FDR: FM
Credits: 3
Planned Offering: Fall, Winter
A study of concepts fundamental to the analysis of finite mathematical structures and processes. These include logic and sets, algorithms, induction, the binomial theorem, and combinatorics.
MATH 122 - Discrete Mathematics II
FDR: SC
Credits: 3
Planned Offering: Offered in the winter term when interest is expressed and departmental resources permit.
Prerequisite: MATH 121. A continuation of MATH 121. Applications of 121 include probability theory in finite sample spaces and properties of the binomial distribution. This course also includes relations on finite sets, equivalence classes, partial orderings, and an introduction to graph theory and enumeration.
MATH 171 - Mathematics of Cryptography
FDR: SC,
Credits: 4
Planned Offering: Spring 2013
Prerequisite: MATH 101 or 121. The history and application of cryptography. Topics include private-key codes, the ENIGMA machine and other WWII codes, public-key codes, and the RSA system. Appropriate mathematics is introduced, as necessary, to understand the construction and use of these codes. Several assignments are themselves in code, and students must decipher them just to find out what the homework is. Dresden.
MATH 195 - Special Topics in Contemporary Mathematics
FDR: SC
Credits: 3
Prerequisite: MATH 101 or 121, depending on course topic. A selected mathematical topic of current widespread interest.
MATH 218 - Applications of Statistics
Credits: 3
Planned Offering: Offered in the winter term when interest is expressed and departmental resources permit.
Prerequisite: MATH 118, MATH 309, or INTR 202. Theory and applications of the General Linear Model, including analysis of variance and covariance, multiple regression, and experimental design.
MATH 221 - Multivariable Calculus
Credits: 3
Planned Offering: Fall, Winter
Prerequisite: The equivalent of MATH 102 with C grade or better. Motion in three dimensions, parametric curves, differential calculus of multivariable functions, multiple integrals, line integrals, and Green’s Theorem.
MATH 222 - Linear Algebra
Credits: 3
Planned Offering: Winter
Prerequisite: MATH 221. Introductory linear algebra: systems of linear equations, matrices and determinants, vector spaces over the reals, linear transformations, eigenvectors, and vector geometry.
MATH 233 - Natural Resource and Electric Grid Modeling
Credits: 4
Planned Offering: Spring 2013
Prerequisite: MATH 102. Mathematical modeling of fish populations in rivers and electric power generation/distribution, two separate but sometimes related systems, the analysis of which can provide essential information for wise policy decision making. Examples of specific questions that might be addressed include: How should a modern electricity grid be designed to minimize loss of electricity and to accommodate use of new energy-generating technologies? How may hydroelectric power generation affect the relationship between native and non-native fish populations in rivers? The class will be divided into teams, each of which will complete an in-depth analysis of one particular question. Crowley.
MATH 270 - Financial and Actuarial Mathematics
Credits: 3
Planned Offering: Winter 2012 and alternate years
Prerequisite: MATH 102. Topics include the time value of money, the force of interest, annuities, yield rates, amortization schedules, bonds, contracts, options, swaps, and arbitrage. Equal emphasis is given to both the theoretical background and to the computational aspects of interest theory. This course helps prepare students for the Financial Mathematics actuary exam. Staff.
MATH 301 - Fundamental Concepts of Mathematics
Credits: 4
Planned Offering: Spring
Prerequisite: Six credits of mathematics or a grade of at least B in MATH 102. Basic analytical tools and principles useful in mathematical investigations, from their beginning stages, in which experimentation and pattern analysis are likely to play a role, to their final stages, in which mathematical discoveries are formally proved to be correct. Strongly recommended for all prospective mathematics majors.
MATH 303 - Complex Analysis
Credits: 3
Planned Offering: Winter 2013 and alternate years
Prerequisite: MATH 221 or consent of the instructor. Algebra of complex numbers, polar form, powers, and roots. Derivatives and geometry of elementary functions. Line integrals, the Cauchy Integral Theorem, the Cauchy Integral formula, Taylor and Laurent Series, residues, and poles. Applications.
MATH 309 - Mathematical Statistics I
Credits: 3
Planned Offering: Fall 2011 and alternate years
Prerequisite: The equivalent of MATH 221 with C grade or better. Probability, probability density and distribution functions, mathematical expectation, discrete and continuous random variables, and moment generating functions.
MATH 310 - Mathematical Statistics II
Credits: 3
Planned Offering: Winter 2012 and alternate years
Prerequisite: MATH 309. Sampling distributions, point and interval estimation, testing hypotheses, regression and correlation, and analysis of variance.
MATH 311 - Real Analysis I
Credits: 3
Planned Offering: Fall
Prerequisites: MATH 221 with C grade or better; MATH 301 is recommended. Basic properties of real numbers, elementary topology of the real line and Euclidean spaces, and continuity and differentiability of real-valued functions on Euclidean spaces.
MATH 312 - Real Analysis II
Credits: 3
Planned Offering: Winter
Prerequisite: MATH 311. Riemann integration, nature and consequences of various types of convergence of sequences and series of functions, some special series, and related topics.
MATH 321 - Abstract Algebra I
Credits: 3
Planned Offering: Fall
Prerequisites: MATH 222; MATH 301 is recommended. Groups, including normal subgroups, quotient groups, permutation groups. Cauchy’s theorem and Sylow’s theorems.
MATH 322 - Abstract Algebra II
Credits: 3
Planned Offering: Winter
Prerequisite: MATH 321. Rings, including ideals, quotient rings, Euclidean rings, polynomial rings. Fields of quotients of an integral domain. Further field theory as time permits.
MATH 332 - Ordinary Differential Equations
Credits: 3
Planned Offering: Fall
Prerequisite: MATH 221 with C grade or better. First and second order differential equations, systems of differential equations, and applications. Techniques employed are analytic, qualitative, and numerical.
MATH 333 - Partial Differential Equations
Credits: 3
Planned Offering: Winter
Prerequisite: MATH 332. An introduction to the study of boundary value problems and partial differential equations. Topics include modeling heat and wave phenomena, Fourier series, separation of variables, and Bessel functions. Techniques employed are analytic, qualitative, and numerical.
MATH 341 - Geometric Topology
Credits: 3
Planned Offering: Fall 2012 and alternate years
Prerequisite: MATH 221. A study of the shape of space focusing on characteristics not detected by geometry alone. Topics are approached pragmatically and include point set topology of Euclidean space, map-coloring problems, knots, the shape of the universe, surfaces, graphs and trees, the fundamental group, the Jordan Curve Theorem, and homology.
MATH 342 - Modern Geometry
Credits: 3
Planned Offering: Winter 2013 and alternate years
Prerequisite: MATH 221. A survey of recent developments in geometry. Topics vary and may include such subjects as the geometry of curves and surfaces, singularity and catastrophe theory, geometric probability, integral geometry, convex geometry, and the geometry of space-time.
MATH 353 - Numerical Analysis
Credits: 4
Planned Offering: Spring 2013 and alternate years
Prerequisites: MATH 221 and 222. Analysis, implementation, and applications of algorithms for solving equations, fitting curves, and numerical differentiation and integration. Theorems and proofs are complemented by hands-on programming exercises fostering a concrete understanding of accuracy, efficiency and stability, as well as an awareness of potential pitfalls in machine arithmetic. No previous programming experience is required. Siehler.
MATH 361 - Graph Theory
Credits: 3
Prerequisite: MATH 122 or 222. Graphs and digraphs, trees, connectivity, cycles and traversability, and planar graphs. Additional topics selected from colorings, matrices and eigenvalues, and enumeration.
MATH 365 - Number Theory
Credits: 3
Planned Offering: Winter 2012 and alternate years.
Prerequisite: MATH 301 or consent of the instructor. Topics include prime numbers, Euclidean algorithm, congruences, Chinese Remainder Theorem, Fermat’s Little Theorem, Euler’s Theorem, arithmetic functions, Euler’s phi function, perfect numbers, the quadratic reciprocity law, continued fractions, and other topics as time and student interest permit.
MATH 369 - The Mathematics of Puzzles and Games
Credits: 4
Planned Offering: Spring 2012 and alternate years
Prerequisite: MATH 322. The application of mathematics to puzzles and games. A brief survey on the designs of tournaments. The puzzles and games include but are not limited to the Rubik’s Cube, poker, blackjack, and peg solitaire. Dymàček.
MATH 383 - Seminar
Credits: 3 in fall and winter, 4 in spring
Planned Offering: Offered when interest is expressed and department resources permit.
Readings and conferences for a student or students on topics agreed upon with the directing staff. May be repeated for degree credit with permission and if the topics are different.
Topic for Winter 2012:
MATH 383-01: Introduction to Mathematical Biology: Population Dynamics, Reaction Kinetics, Physiology and Neuroscience (3). Prerequisite: MATH 102. Recommended: BIOL 111. In this course, we use continuous dynamical systems in order to model a spectrum of biological problems in areas to include: population dynamics; chemical reaction kinetics; physiology; and neuroscience. A primer is given on differential equations and numerical simulation. We then utilize ordinary differential equations to model dynamics that arise in these biological areas so as to tease out the mechanisms underlying the phenomena and use the models to aid in making experimental predictions. The course introduces ideas from perturbation methods and bifurcation theory; and, if time allows, includes discussion of discrete processes and spatial modeling (partial differential equations). Oster. Note: Note: Seminar and research offerings are contingent upon the demonstrated need and aptitude of the student for independent work in mathematics and upon the availability of departmental resources.
MATH 401 - Directed Individual Study
Credits: 1
Prerequisite: Consent of the department. Individual conferences. May be repeated for degree credit with permission and if the topics are different.
MATH 402 - Directed Individual Study
Credits: 2
Prerequisite: Consent of the department. Individual conferences. May be repeated for degree credit with permission and if the topics are different.
MATH 403 - Directed Individual Study
Credits: 3
Prerequisite: Permission of the department. Individual conferences. May be repeated for degree credit with permission and if the topics are different.
MATH 421 - Directed Individual Research
Credits: 1
Prerequisite: Permission of the department. Directed independent work in mathematics, especially for honors candidates. May be repeated for degree credit with permission and if the topics are different.
MATH 422 - Directed Individual Research
Credits: 2
Prerequisite: Permission of the department. Directed independent work in mathematics, especially for honors candidates. May be repeated for degree credit with permission and if the topics are different.
MATH 423 - Directed Individual Research
Credits: 3
Prerequisite: Permission of the department. Directed independent work in mathematics, especially for honors candidates. May be repeated for degree credit with permission and if the topics are different.
MATH 426 - Directed Individual Research
Credits: 6
Prerequisite: Permission of the department. Directed independent work in mathematics, especially for honors candidates. May be repeated for degree credit with permission and if the topics are different.
MATH 493 - Honors Thesis
Credits: 3-3
Planned Offering: Fall-Winter
Prerequisites: Honors candidacy, senior standing and consent of the department. Honors Thesis.
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