The courses described below are offered by the Department of Mathematical Sciences of the McMicken College of Arts & Sciences, University of Cincinnati. These descriptions should not be construed as syllabi for the courses.
Each description includes the course name, the course number, credit hours, pre- and/or co-requisites, quarters offered (subject to change depending on demand), and textbook title(s), when available.
Explanation of Course Numbers
Each course number is a nine-character University code. The first two digits specify the college offering the course (“15” = College of Arts & Sciences); the next four letters indicate the area of study; the final three digits identify the specific course. Honors classes have an “H”
at the end. Courses marked '500' or higher are typically graduate level classes.
Example:
15 MATH 252 H
Honors Calculus II
McMicken Mathematics Requirements
Any of the following entry-level sequences will satisfy the mathematics requirement of the College of Arts & Sciences:
Elementary Probability and Statistics
15 MATH 147, 148, 149
Topics in Mathematics
15 MATH 155, 156, 157
Applied Calculus
15 MATH 224, 226, 227
Finite Math & Applied Calculus
15 MATH 225, 226, 227
Calculus I, II
15 MATH 251, 252
Course Descriptions
STATISTICS FOR THE HEALTH SCIENCES
15 MATH 146
3 UG CR
Prerequisite:
Two years of high school algebra. MPT score of 420 or above recommended.
Text:
Knapp, R.G., Basic Statistics for Nurses, 2nd Edition
Statistical models and inference applied to problems in the health sciences, with emphasis on the role that statistics plays in medical research. Primarily for students in the College of Nursing and Health. Win. Qtr.
(offered on Sat. in Aut. Qtr)
ELEMENTARY PROBABILITY AND STATISTICS I, II, III
15 MATH 147, 148, 149
3 UG CR ea. qtr. (May be used for the 9-credit A&S mathematics requirement.)
Prerequisite:
Knowledge of high school algebra. MPT score of 420 or above recommended.
Text:
Moore and McCabe, Introduction to the Practice of Statistics, 5th Edition
15 MATH 147
Chapters 1-4. DATA: Distributions and graphs, summarizing data, normal distribution, scatterplots, designing samples and experiments, probability. Aut., Sum. Qtrs
15 MATH 148
Chapters 4-7. PROBABILITY AND INFERENCE: Sampling distributions, probability, binomial distribution, confidence intervals, inference for means, comparing two means. Win., Sum. Qtrs.
15 MATH 149
Chapters 7-13. TOPICS IN INFERENCE: Inference for proportions, two-sample inference, two-way tables and Chi Square, one-way analysis of variance (ANOVA), inference for regression. Spr., Sum. Qtrs.
HONORS ELEMENTARY PROBABILITY AND STATISTICS I, II, III
15 MATH 147H, 148H, 149H
3 UG CR ea. qtr. (May be used for the 9-credit A&S mathematics requirement.)
Prerequisite:
University Honors Scholars; Knowledge of high school algebra.
Text:
Moore and McCabe, Introduction to the Practice of Statistics, 5th Edition
15 MATH 147H
Honors version of 15 Math 147. Chapters 1-7. UNDERSTANDING DATA: Distributions and graphs, summarizing data, normal distribution, scatterplots, catagorical data, designing samples and experiments, probability.
Aut Qtr.
15 MATH 148H
Honors version of 15 Math 148. Chapters 8-11. UNDERSTANDING INFERENCE: Sampling distributions, probability, sample portions and means, binomial distribution, confidence intervals, inference for means, comparing two means, inference for population spread. Win Qtr.
15 MATH 149H
Honors version of 15 Math 149. Chapters 12-15. TOPICS IN INFERENCE: Inference for proportions, two-sample inference, two-way tables and Chi Square, one-way analysis of variance (ANOVA), inference for regression. Spr Qtr.
TOPICS IN MATHEMATICS I, II, III
15 MATH 155, 156, 157
3 UG CR ea. qtr. (May be used for the 9-credit A&S mathematics requirement.)
Prerequisite:
Two years of high school mathematics (algebra and plane geometry) or the equivalent. MPT score of 420 or above recommended. Courses may be taken in any order.
3 UG CR ea. qtr. (Cannot be used for the 9-credit A&S mathematics requirement. This sequence is intended for students who need preparation for a college-level calculus course.)
Prerequisite:
Two years of high school mathematics (algebra and plane geometry) or the equivalent. Note: Math 173 or a score of 500 of better on the Math Placement Exam is prerequisite for Math 174.
Text:
Swokowski, Algebra & Trigonometry, 11th edition.
15 MATH 173
Review of basic algebra. Graphing, quadratic equations, linear and nonlinear inequalities, modeling, functions. Aut., Wtr, Spr, Sum. Qtrs.
15 MATH 174
Inverse functions; polynomial, rational, exponential and logarithmic functions, systems of linear equations, systems of inequalities. Aut, Wtr., Spr, Sum. Qtrs.
COLLEGE ALGEBRA (ACCELERATED)
15 MATH 176
3 UG CR Discontinued. Replaced by 15 MATH 224
Prerequisite:
Text:
TRIGONOMETRY
15 MATH 181
3 UG CR (Cannot be used for the 9-credit A&S mathematics requirement. This course is intended for students who preparing for the 5-credit hour calculus sequence.)
Prerequisite:
MATH 176, MATH 174, or equivalent. MPT score of 530 or above recommended.
Text:
Stewart, Redlin & Watson, Algebra and Trigonometry.
Chapters 7, 8, 9, 11. Right triangle trigonometry, laws of sines and cosines, trigonometric functions and graphs, trigonometric identities, vectors, conic sections, polar coordinates. Aut, Spr, Sum Qtrs.
FINITE MATHEMATICS
15 MATH 182
3 UG CR No longer offered. Replaced by 15 MATH 225
Prerequisite:
Text:
COOPERATIVE LEARNING IN CALCULUS 0, I, II, III, IV
15 MATH 200, 201, 202, 203, 204
1 UG CR ea. qtr
Co-requisite:
Registration in corresponding Calculus class
Text:
BOOK NOT REQUIRED (Text based on book from Calculus 0, I, II, III).
15 MATH 200
Guided group work to complement the Calculus 0 curriculum. Aut. Qtr. only
15 MATH 201
Guided group work to complement the Calculus I curriculum. Aut., Win. Qtrs.
15 MATH 202
Guided group work to complement the Calculus II curriculum. Win., Spr. Qtrs.
15 MATH 203
Guided group work to complement the Calculus III curriculum. Spr., Sum. Qtrs.
15 MATH 204
Guided group work to complement the Calculus IV curriculum. Aut. Qtr. only
FOUNDATIONS OF APPLIED CALCULUS, FINITE MATH, APPLIED CALCULUS I, II
15 MATH 224, 225, 226, 227
3 UG CR ea. qtr. Either 224, 226, 227 or 225, 226,227,can be used for the 9-credit A&S mathematics requirement.
15 MATH 224
Foundations of Applied Calculus. Review of algebraic skills needed for calculus, including exponents, radicals, linear equations and inequalities, linear systems and exponential and logarithm functions. Aut., Sum. Qtrs. (Win., Spr., evenings only)
Prerequisite:
A score of 470 or better on the Math Placement Test.
Text:
Warren B. Gordon, Succeeding in Applied Calculus
15 MATH 225
Finite Mathematics
Prerequisite:
A score of 530 or better on the Math Placement Test is required for 15 Math 225 (which is a prerequisite for 15 Math 226)
Text:
Prerequisite:
Grade of C- or above on Math 224 or 225. Score of 670 or above on MPT.
L. Goldstein, D. Lay, and D. Schneider, Brief Calculus and Its Applications, 10th Edition
15 MATH 227
Applied Calculus 2. Applications of exponential and logarithm functions, antidifferentiation, the definite integral, area, functions of two variables, partial derivatives, maxima and minima, Lagrange multipliers. Win., Spr., Sum. Qtrs. (Aut, evenings only)
Text:
L. Goldstein, D. Lay, and D. Schneider, Brief Calculus and Its Applications, 10th Edition
FINITE ALGEBRA AND FINITE MATH, CONCEPTS OF CALCULUS
15 MATH 228, 229
3 UG CR ea qtr
Prerequisite:
Math 174, Math 176 or Math 224 or a score of 530 or better on the Mathematics Placement Exam.
College of Business students only.
Text:
Waner and Costenoble, Finite Mathematics and Applied Calculus, 3rd edition.
15 MATH 228
Appendix A, Chapters 1-7 (excl. 1.5, 3.4, 4.4, 4.5, 5.3, 7.7), Chapter 10 (sec. 1,2,3). Review of algebra, linear functions, systems of linear equations, matrix algebra, linear programming, sets and counting, probability, nonlinear models. This course incorporates laboratory sessions using Excel or Derive software. Aut., Wtr, Spr, Sum. Qtrs.
15 MATH 229
Chapters 11-14 and Chapter 15 (secs. 1,2,5). The derivative, techniques of differentiation, applications of the derivative. Definite, indefinite, improper integrals, applications of the integral. This course incorporates laboratory sessions using Excel or Derive software. Aut, Wtr., Spr, Sum. Qtrs.
HONORS FINITE MATHEMATICS & CALCULUS I, II, III
15 MATH 225H, 226H, 227H
3 UG CR ea. qtr. Can be used for the 9-credit A&S mathematics requirement.
Prerequisite:
University Honors scholars and students in Honors Plus Program.
15 MATH 225H
Topics from Finite Math, such as solving systems of linear equations, matrices, linear programming. Aut. Qtr.
Text:
Warren B. Gordon, Succeeding in Applied Calculus
15 MATH 226H
Honors version of 15 MATH 226. Win. Qtr.
Text:
L. Goldstein, D. Lay, and D. Schneider, Brief Calculus and Its Applications, 9th Edition
15 MATH 227H
Honors version of 15 MATH 227. Spr. Qtr.
Text:
L. Goldstein, D. Lay, and D. Schneider, Brief Calculus and Its Applications, 9th Edition
CALCULUS 0
15 MATH 250
5 UG CR
Prerequisite:
A score of 550 or better on the Math Placement Test.
Text:
Faires, Pre-Calculus
Pre-Calculus topics for students who need more preparation before entering 251. Aut., Win., Sum. Qtrs.
CALCULUS I, II, III
15 MATH 251, 252, 253
Math 251, 5 UG CR ea. qtr. Math 252 & 253, 4 UG CR ea. qtr. 15 MATH 251, 252 may be used to satisfy the A&S mathematics requirement.
Prerequisite:
Calculus 251: a score of 670 or better on the Math Placement Test OR a C- or better in 15 MATH 250. A passing grade in the previous-numbered Calculus course is required to take the next sequential Calculus course.
Text:
Stewart, Calculus Concepts and Contexts, 3rd Edition
15 MATH 251
Functions, limits and continuity, derivatives, applications of the derivative, antiderivatives. Aut., Win., Spr. Qtrs. (5 CR) (Eves in Sum.)
15 MATH 252
The integral, inverse functions, techniques of integration, applications of the integral. Win., Spr, Sum. Qtrs. (Eves in Aut.)
15 MATH 253
Sequences and series, vectors, lines and planes, vector-valued functions. Aut., Spr., Sum. Qtrs. (Eves in Win.)
HONORS CALCULUS I, II, III
15 MATH 251H, 252H, 253H
Math 251, 5 UG CR ea. qtr. Math 252 & 253, 4 UG CR ea. qtr.
Prerequisite:
University Honors scholars with placement score of 860 or better on the Math Placement Test or advanced placement. A passing grade in the previous-numbered Calculus course is required to take the next sequential Calculus course.
Text:
Stewart, Calculus Concepts and Contexts, 3rd Edition
15 MATH 251H
Honors version of 15 MATH 251. Aut. Qtr.
15 MATH 252H
Honors version of 15 MATH 252. Win. Qtr.
15 MATH 253H
Honors version of 15 MATH 253. Spr. Qtr.
CALCULUS LABS II, III
15 MATH 256, 257, (258)
1 UG CR ea. qtr
Text:
Stewart, Calc Lab with Mathematica, 2nd Edition
15 MATH 256
Calc II Lab to accompany Calculus II (Co-requisite: Calculus 252.) Win., Spr., Sum. Qtrs. (Eves in Aut.)
15 MATH 257
Calc III Lab to accompany Calculus III (Co-requisite: Calculus 253.)
Aut., Spr., Sum. Qtrs. (Eves in Win.)
15 MATH 258
Calc IV Lab to accompany Calculus IV . Discontinued.
CALCULUS IV
15 MATH 264
5 UG CR ea. qtr
Pre-requisite:
Calculus III (15 MATH 253).
Text:
Stewart, Calculus Concepts and Contexts, 3rd Edition
Calculus III (15 MATH 253) and Honors Scholars status.
Honors version of 15 Math 264. Partial derivatives, multiple integrals, calculus of vector fields. Aut. Qtr.
DIFFERENTIAL EQUATIONS
15 MATH 273
5 UG CR
Prerequisite:
Calculus III (15 MATH 253).
Text:
Boyce & DiPrima, Elementary Differential Equations with Boundary Value Problems, 8th Edition.
First-order linear differential equations, first-order separable differential equations, first-order homogeneous differential equations, exact differential equations, linear dependence for solutions of a second-order linear
homogeneous differential equation, Wronskians, second-order linear homogeneous differential equations with constant coefficients, method of undetermined coefficients, method of variation of parameters, series expansions of solutions of second-order linear differential equations at ordinary
points, Euler equations, introduction to regular singular points, higher-order linear differential equations, higher-order linear homogeneous differential equations with constant coefficients, the method of undetermined coefficients, Laplace transform. Aut., Win., Spr., Sum. Qtrs.
MATRIX METHODS
15 MATH 276
3 UG CR Credits may not be applied toward a degree in mathematics
Prerequisite:
Calculus III (15 MATH 253).
Text:
Bronson, Matrix Methods, 2nd Edition.
Matrices, systems of linear equations, Gaussian elimination, determinants, computation of inverses, eigenvalues and eigenvectors, coordinate transformations, systems of differential equations,
applications to mechanical systems and electrical circuits.
Aut., Win., Spr., Sum. Qtrs.
NUMBER SENSE & NUMBER RELATIONS FOR TEACHERS
15 MATH 300
3 UG CR
Prerequisite:
15 Math 226 (Finite Math & Calculus II)
Text:
TBA
This inquiry-based course will deal with the application of concepts of number, number theory, and number systems. Students will learn to apply numerical computation and estimation techniques and extend them to algebraic expressions.
The will investigate the concepts of proportional reasoning, ratios, and fractions and explore various methods of problem-solving in order to obtain a profound fundamental understanding of mathematics relevant to and necessary for mathematics education in grades 5 – 12. Spr. Qtr.
NUMBER & FORM: An Historical Survey for Teachers
15 MATH 301
3 UG CR
Prerequisite:
15 Math 300 (Number Sense) and 15 Math 227 (Finite Math & Calculus III) or permission of instructor.
Text:
Bedient, The Historical Roots of Elementary Mathematics
This course develops some of the principle themes of elementary mathematics (arithmetic and a bit of algebra and geometry) in an historical context. The Egyptian, Sumerian, Mayan, Hindu/Arabic, and binary number
systems will be studied in some detail and the connection of number with form in Babylonian geometric algebra and early Greek mathematics – through the notion of incommensurability – will be explored. Inquiry-based group activities are an integral feature of the course. Aut.
Qtr.
ALGEBRA FOR MIDDLE SCHOOL TEACHERS
15 MATH 303
3 UG CR
Prerequisite:
15 MATH 301 (Number & Form) and 15 MATH 227 (Finite Math & Calculus III)
Text:
TBA
This inquiry-based course will deal with algebra as an extension of arithmetic, as a means of describing real situations, and as a means of solving problems as well as considering the connections between algebra
and geometry. Win. Qtr.
GEOMETRY FOR TEACHERS
15 MATH 305
3 UG CR
Prerequisite:
15 Math 227 (Finite Math & Calculus III) and 15 Math 303 (Algebra for Teachers) or permission of instructor.
Text:
NO BOOK NEEDED – Using Professor’s Notes
This course will deal with aspects of geometry, including shapes, measurement, and transformations, providing the deeper understanding of geometry that is needed to teach the subject and to illustrate connections
between geometry and other parts of mathematics. Dynamical geometry software, Geometers Sketchpad, will be introduced. Spr. Qtr
LINEAR ALGEBRA I, II
15 MATH 351, 352
3 UG CR ea. qtr.
Prerequisite:
Calculus III (15 MATH 253)
Text:
Wright, Introduction to Linear Algebra (Special Edition)
15 MATH 351.
Linear equations, matrices, Euclidean n-space and its subspaces, bases, dimension, coordinates. Aut., Sum. Qtrs. (Eves in Win.)
15 MATH 352
Orthogonality, linear transformations, determinants, eigenvalues and eigenvectors, diagonalization. Win., Sum. Qtrs. (Eves in Spr.)
INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS
15 MATH 355.
3 UG CR
Prerequisite:
Calculus III (15 MATH 253) and Linear Algebra II (15 MATH 352).
Text:
Braun, M., Differential Equations and Their Applications.
First order differential equations. Linear differential equations of higher order. Differential operators and systems of linear differential equations. Spr. Qtr.
INTRODUCTION TO ABSTRACT MATHEMATICS
15 MATH 357
3 UG CR
Prerequisite:
Linear Algebra II (15 MATH 352).
Text:
Smith, Eggan, St. Andre, A Transition to Advanced Math, 6th Edition
Logic, proofs, set theory, relations, functions, cardinality. Spr. Qtr. (Eves in Aut.)
PROBABILITY AND STATISTICS I, II, III
15 MATH 361, 362, 363
3 UG CR ea. qtr.
Prerequisite:
Calculus III (15 MATH 253)
Text:
Walpole & Myers, Probability and Statistics for Engineers and Scientists, 7th Edition.
15 MATH 361
Chapters 1-7. Sample statistics. Probability, sample spaces, counting rules conditional probability. Discrete and continuous random variables, their distributions and expected values, Binomial, Poisson, hypergeometric,
normal and gamma distributions. Covariance, correlation. Sampling distributions of means and sums. Aut., Win., Spr., Sum. Qtrs.
15 MATH 362
Chapters 8-11. Point estimation, confidence intervals for means, proportions, variances and differences of means and proportions. Hypothesis testing. Chi-square tests. Simple linear regression. Model building. SAS
computer package. Win., Spr., Sum. Qtrs.
15 MATH 363
Chapters 11-15. More linear regression, multiple linear regression, analysis of variance, experimental design, reliability, and quality control. SAS computer package. Spr. Qtr.
ENGINEERING STATISTICS
15 MATH 366
3 UG CR Credits may not be applied toward a degree in mathematics.
Prerequisite:
Calculus III (15 MATH 253)
Text:
Hogg and Ledolter, Engineering Statistics.
Descriptive statistics, probability, binomial, Poisson, and normal distributions. Confidence intervals, and hypothesis testing, regression analysis. Win., Spr. Qtrs.
APPLIED BOUNDARY VALUE PROBLEMS
15 MATH 377
3 UG CR Credits may not be applied toward a degree in mathematics.
Prerequisite:
Calculus IV (15 MATH 254) and Differential Equations (15 MATH 273).
Fourier series, partial differential equations. Boundary value problems and engineering applications. Spr. Qtr.
INTRODUCTION TO ALGEBRA
15 MATH 401, 402
3 UG CR ea. qtr.
Prerequisite:
Introduction to Abstract Mathematics (15 MATH 357).
Text:
Hungerford, Abstract Algebra, An Introduction, 2nd Edition.
15 MATH 401
Prime numbers, integer factorization, modular arithmetic, rings, homomorphisms. Factorization of polynomials. Aut. Qtr.
15 MATH 402
Introduction to the theory of groups. Wtr. Qtr.
HISTORY OF MATHEMATICS
15 MATH 404.
3 UG CR ea. qtr.
Prerequisite:
Introduction to Geometry I (15 MATH 406).
Text:
Burton, The History of Mathematics: An Introduction, 4th Edition.
15 MATH 404
A survey of the history of mathematics from ancient times through the invention of the calculus. Egyptian and Babylonian computational systems, Pythagoreanism, Euclid, the work of Archimedes, Hindu-Arabic numeration
and algebra, the algebra of the Renaissance, Galileo’s mathematization of nature, the geometry of Descartes and Fernat, the calculus of Newton and Leibniz. Spr. Qtr.
INTRODUCTION TO GEOMETRY I, II
15 MATH 406, 407
3 UG CR ea. qtr.
15 MATH 404
An axiomatic treatment of synthetic geometry is given, beginning with a development of neutral geometry. Neutral geometry is geometry without the Parallel Postulate, so the theorems of neutral geometry are valid
in both hyperbolic and Euclidean geometry. The formal development of Euclidean geometry begins with the addition of the Parallel Postulate. The main tools in Euclidean geometry are congruence and similarity of figures; triangles, quadrilaterals, and circles are studied in detail. Aut. Qtr.
Prerequisite:
Intro to Abstract Math (15 MATH 357)
Text:
NO BOOK NEEDED
15 MATH 407
Vector methods provide and alternate context for developing geometry. The vector algebraic approach brings together linear algebra, geometry, and trigonometry. Affine geometry is studied in the context of vector
spaces, the inner product is added to the vector space axioms for the study of Euclidean geometry. Transformations give a third method to treat geometry and illustrate connections between geometry, linear algebra, and abstract algebra. Affine transformations are used to investigate affine
geometry. Isometries and similarities are used for the study of Euclidean geometry. Symmetry is considered in terms of the group of rigid motions that leave invariant a geometric figure. Transformation groups and symmetry groups provide connections with abstract algebra. Win. Qtr.
Prerequisite:
Intro to Geometry I (15 MATH 406)
Text:
Berele and Goldman, Geometry: Theorems and Constructions, 1st Edition
INTRODUCTION TO ANALYSIS I, II
15 MATH 408, 409
3 UG CR ea. qtr.
15 MATH 408
The Real and Rational Number Systems: algebraic, order and completeness properties; Sequences: boundedness, monotonicity, convergence; Limits of Real-valued Functions; Continuous Functions: local and global properties,
Intermediate Value Theorem. Win. Qtr.
Prerequisite:
Introduction to Abstract Math (15 MATH 357)
Text:
Wright, duplicated notes
15 MATH 409
The Derivative: differentiation of algebraic and basic transcendental functions, Mean Value Theorem, applications of the derivative to analyze monotonicity, convexity, and local extrema, Taylor’s Theorem; The
Riemann Integral: algebraic properties, Fundamental Theorem of Calculus. Infinite Series: convergence tests, absolute and conditional convergence, power series. Spr. Qtr.
Prerequisite:
Introduction to Analysis I (15 MATH 408)
Text:
Wright, duplicated notes
DISCRETE MATH & ITS APPLICATIONS
15 MATH 410
3 UG CR Credits may not be applied toward a degree in mathematics.
Prerequisite:
Calculus III (15 MATH 253) and Probability & Stats I (15 MATH 361)
Text:
Rosen, Discrete Math & Its Applications, 5th Edition
Completion of both Introduction to Ordinary Differential Equations (15 MATH 355) and Introduction to Abstract Mathematics (15 MATH 357) and at least a 3.0 math GPA.
Text:
NO BOOK NEEDED
Practical work-related experience in a supervised internship where job responsibilities involve statistical or mathematical reasoning or computation.For math majors or math as a second major. Must be coordinated
with a mathematical sciences faculty member and approved by the Undergraduate Program Director. Credit to be awarded varies and depends on work experience. Credit does not count toward the 61 necessary for the major/second major. Aut., Win., Spr., Sum. Qtrs.
SENIOR CAPSTONE EXPERIENCE IN MATHEMATICAL SCIENCES
15 MATH 501
1 UG CR
Prerequisite:
Senior standing in mathematics.
Text:
NO BOOK NEEDED
For math majors/second majors to get credit for the completion of their (required) senior capstone project or capstone course work. The actual capstone experience is individually selected by students with approval
of the Undergraduate Program Director. Aut., Win., Spr., Sum. Qtrs.
ADVANCED CALCULUS I, II, III
15 MATH 504, 505, 506
3 UG or GR CR ea. qtr.
Prerequisite:
Calculus IV (15 MATH 254), Introduction to Ordinary Differential Equations (15 MATH 355), and Introduction to Abstract Mathematics (15 MATH 357).
Text:
Rosenlicht, Introduction to Analysis
Gordon, Real Analysis - A First Glance, 2nd Edition
15 MATH 504
Ordered sets, the real field, the complex field, Euclidean space, finite, countable and uncountable sets, metric spaces, compact sets, convergent sequences of numbers, Cauchy sequences, upper and lower limits, Bolzano-Weierstrass
theorem, series, the number e, convergence tests for series, absolute convergence, addition and multiplication of series, rearrangements. Aut. Qtr.
15 MATH 505
Limits and continuity of functions, continuity and compactness, connectedness and continuity, discontinuities, monotone functions, derivatives, the Mean Value theorem, l'Hopital's rule, higher order derivatives,
Taylor's theorem, Riemann-Stieltjes integral, integration and differentiation of vector-valued functions, rectifiable curves. Win. Qtr.
15 MATH 506
Uniform convergence for sequences and series of functions, equi-continuous families of functions, the Stone-Weierstrass theorem, functions of several variables. Spr. Qtr.
ABSTRACT ALGEBRA I, II, III
15 MATH 511, 512, 513
3 UG or GR CR ea. qtr.
Prerequisite:
Linear Algebra II (15 MATH 352), Introduction to Abstract Mathematics (15 MATH 357). Sequence may be started with either 511 or 512 (i.e. 511 is not a prerequisite for 512; however, 512 is a prerequisite for
513).
Text:
Lang, Linear Algebra, 3rd Edition. (Text for 15 MATH 511 only)
15 MATH 511
Advanced Linear Algebra: Abstract vector spaces, determinants, eigenvalues and eigenvectors, algebra of linear transformations, canonical forms including triangular, Jordan and rational forms. Aut. Qtr.
Text:
Goodman, Algebra: Abstract and Concrete (Text for 15 MATH 512 and 15 MATH 513)
15 MATH 512
Definition and basic properties of groups, subgroups, permutation groups, direct products, isomorphisms, homomorphisms, normal subgroups and factor groups. Win. Qtr.
15 MATH 513
Selected topics in number theory. Binary relations and binary operations. Definitions and basic properties of rings and fields, integral domain, quotient fields, quotient rings and ideals, factorization of polynomials
over fields, unique factorization domains, Euclidean domains, Gaussian integers, extension fields, algebraic extensions, geometric constructions, finite fields. Spr. Qtr.
NUMERICAL ANALYSIS I, II, III
15 MATH 514, 515, 516
3 UG or GR CR ea. qtr.
Prerequisite:
Calculus IV (15 MATH 254); Differential Equations (15 MATH 273) or Introduction to Ordinary Differential Equations (15 MATH 355); Matrix Methods (15 MATH 276) or Linear Algebra II (15 MATH 352); a working knowledge
of some programming language.
Chapters 1, 4, 5. Introduction to a floating point arithmetic, roundoff error, error propagation.Solution of non-linear equations by bisection, secant, regula-falsi, and Newton methods with emphasis on error analysis
and utility of computations. Polynomial interpolation, error bounds and the Runge phenomenon. Cubic spline interpolation and extremal properties. Orthogonal polynomials and least squares approximation.Computer applications. Aut. Qtr.
15 MATH 515
Chapters 2, 4. Gauss elimination, pivoting strategies. Error analysis and vector norms. Iterative methods for linear systems including Jacobi and Gauss-Seidel methods. Eigenvalue-eigenvector computations by power,
inverse power, and Rayleigh quotient methods. Householder transformations, Hessenberg matrices and the Q-R method. The singular value decomposition and least squares problems. Computer applications. Win. Qtr.
15 MATH 516
Chapters 6, 7, 8. Numerical differentiation. Newton-Cotes and Gaussian quadrature, Romberg integration, FFT, Adaptive quadrature. Numerical methods for initial value ordinary differential equations including methods
of Runge-Kutta type and predictor-corrector methods. Stability, consistency, and convergence are analyzed. Finite difference methods for two-point boundary value problems. Decent methods for optimization problems. Computer applications. Spr. Qtr.
APPLIED MATHEMATICS PRACTICUM
15 MATH 517, 518, 519
3 UG or GR CR ea. qtr.
Prerequisite:
Calculus IV (15 MATH 254), Differential Equations (15 MATH 273), and computer programming experience.
Text:
TBA
15 MATH 517
Techniques in applied mathematics; ordinary and partial differential equations, numerical methods, perturbation techniques, modeling. Under the guidance of the instructor, teams of students solve problems from industry,
government, etc. and present reports on their findings. Offered variable quarters.
15 MATH 518
A continuation of 15 MATH 517.
15 MATH 519
A continuation of 15 MATH 518.
MATHEMATICAL STATISTICS I, II, III
15 MATH 521, 522, 523
3 UG or GR CR ea. qtr.
Prerequisite:
Calculus IV (15 MATH 254) and Probability and Statistics I (15 MATH 361).
Text:
Hogg, McKean, and Craig, Introduction to Mathematical Statistics, 6 th Edition.
15 MATH 521
Chapters 1, 2, 3 (through 3.4). Random variables, probability distribution functions, mathematical expectation, inequalities, moment-generating functions, transformation of variables, marginal and conditional distributions, independence, binomial, Poisson, Gamma and normal distributions.
Aut. Qtr.
15 MATH 522
Chapters 3 (starting 3.5), 4, 5. Multivariate Normal, t- and F- distributions, sampling distributions: , order statistics, , distribution of sample mean and sample variance, stochastic convergence, central limit theorem, , , confidence intervals, hypothesis testing, chi-square tests, Monte Carlo methods, bootstarp. Win. Qtr.
15 MATH 523
Chapters 6, 7,8. , Uniformly most powerful tests, likelihood ratio tests, sufficient statistics, Rao-Blackwell theorem, exponential family , Rao-Cramer bound , sequential tests, minimax and classification procedure. Spr. Qtr.
LINEAR PROGRAMMING I, II
15 MATH 524, 525
3 UG or GR CR ea. qtr.
Prerequisite:
Calculus IV (15 MATH 254); Linear Algebra II (15 MATH 352)
Text:
TBA
15 MATH 524
The simplex method (initialization, iteration, termination, sensitivity), the revised simplex method, duality, complementary slackness, the transportation problem, applications. Win. Qtr.
15 MATH 525
The transshipment problem, caterer problem, networks, max flow/min cut, matching problems, primal dual algorithm, Ford-Fulkerson algorithm, integer programming (cutting planes and branch and bound), interior point
methods (ellipsoid method, Karmarkar’s method), applications. Spr. Qtr.
NON-LINEAR OPTIMIZATION
15 MATH 526
3 UG or GR CR
Prerequisite:
Calculus IV (15 MATH 254)
Text:
TBA
Methods of unconstrained optimization, the steepest descent method, Newton’s Method, conjugate direction methods, quasi-Newton and variable metric methods, theory and methods of constrained penalty methods.
Spr. Qtr.
APPLIED STATISTICAL INFERENCE
15 MATH 531
3 UG or GR CR
Prerequisite:
Calculus IV (15 MATH 254) and Linear Algebra II (15 MATH 352)
Text:
Milton and Arnold, Introduction to Probability and Statistics, 4th Edition.
Quick review of probability distributions. Inferences about population means and variance. Aut., Sum. Qtrs.
APPLIED REGRESSION ANALYSIS
15 MATH 532
3 UG or GR CR
Prerequisite:
Applied Statistical Inference (15 MATH 531) or Probability and Statistics I and II (15 MATH 361, 362)
Text:
Neter, Applied Linear Statistical Models; SAS System for Linear Models, 3rd Edition.
Correlation and multiple regression.One-way ANOVA and multiple comparisons. Projects using SAS packages. Win., Sum. Qtrs.
ANALYSIS OF VARIANCE
15 MATH 533
3 UG or GR CR
Prerequisite:
Applied Regression Analysis (15 MATH 532)
Text:
Neter, Applied Linear Statistical Models; SAS System for Linear Models, 3rd Edition.
ANOVA for some standard experimental designs and unbalanced designs. Repeated measures and the analysis of covariance. Spr. Qtr.
SAS PROGRAMMING
15 MATH 534
3 UG or GR CR
Prerequisite:
Applied Regression Analysis (15 MATH 532) ~ can be taken concurrently.
Text:
Delwiche & Slaughter, The Little SAS Book
Carpenter, CarpenterÕs Guide to the SAS Macro
This course will study various aspects of the SAS statistical package from a programming language perspective. It will emphasize the SAS data steps including the infile, input, merge, set, do-loop, if-then commands,
etc. SAS mathematical, statistical, and data functions are discussed, as well as learning to write MACROs and how to do extensive matrix computations using PROC IML, also PROC INSIGHT, and the high resolution graphics procedures. The concentration is on programming issues rather than on
statistical procedures; however, several statistical procedures are discussed and illustrated. Win., Sum. Qtrs.
APPLIED STATISTICS USING S-PLUS
15 MATH 535
3 UG or GR CR
Prerequisite:
Probability and Statistics (15 MATH 361, 362, 363) or Applied Statistical Inference (15 MATH 531) or Applied Regression Analysis (15 MATH 532) or Analysis of Variance (15 MATH 533).
Text:
TBA
To obtain and enhance statistical analysis and programming skills using S-Plus. Various modern techniques in linear statistical modeling, write statistical functions, create graphs. Spr. Qtr.
PROBABILISTIC ASPECTS OF FINANCIAL MODELING
15 MATH 540
3 UG or GR CR
Prerequisite:
Probability & Statistics (15 MATH 361) or Mathematical Statistics I (15 MATH 521). Applied Probability and Stochastic Processes (15 MATH 577) recommended.
Text:
TBA
An introduction to the mathematical theory behind discrete and continuous time financial models. Covers martingales, martingales measures, change of measure, martingale representation, and Black Scholes formula.
COMPUTATIONAL FINANCIAL MATHEMATICS I, II, III
15 MATH 541, 542, 543
3 UG or GR CR ea qtr.
Prerequisite:
Calculus IV (15 MATH 254), Differential Equations (15 MATH 273), Matrix Methods (15 MATH 276), Probability & Statistics (15 MATH 361) or equivalent courses. 15 MATH 541 is a prerequisite for 15 MATH 542; 15 MATH 542
is a prerequisite for 15 MATH 543.
Text:
Stojanovic, Computational Financial Mathematics Using Mathematica
15 MATH 541
Symbolic and numerical solutions of ODEs, Brownian motion, stochastic calculus, Black Scholes formula, computer lab using Mathematica. Aut. Qtr.
15 MATH 542
Stock market statistics, Bayesian and non-Bayesian estimates, implied volatility, numerical PDEs, optimal control of PDEs. Computer lab using Mathematica. Win. Qtr.
15 MATH 543
American options, optimal stopping, Dupire PDE, portfolio rules, portfolio optimization, computer lab using Mathematica. Spr. Qtr.
NUMBER THEORY
15 MATH 551
3 UG or GR CR ea. qtr.
Prerequisite:
Intro. To Algebra I, II (15 MATH 401, 402)
Text:
Joseph Silverman, A Friendly Introduction to Number Theory, 2nd Edition
