|
About the Department
Undergrad Studies
Graduate Studies
Research
Faculty & Staff
News & Events
Alumni & Friends
Course Information
Description of
Courses
Schedule of Courses
Course Web Sites
Math Placement Test
Electronic Reserves
Statistical Consulting
Mathematics Learning
Center
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Course
Descriptions
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 are designated by an “H” in
the course number. Course numbers of 500 or higher are typically graduate-level
classes.
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Example:
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15 MATH 252 H
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Honors Calculus II
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McMicken Mathematics Requirements
Any of the following entry-level sequences will satisfy the mathematics
requirement of
the College of Arts & Sciences:
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Elementary Probability and Statistics
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15 MATH 147, 148, 149
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Topics in Mathematics
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15 MATH 155, 156, 157
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Applied Calculus
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15 MATH 224, 226, 227
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Finite Math & Applied Calculus
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15 MATH 225, 226, 227
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Calculus I, II
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15 MATH 251, 252
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Course Descriptions
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STATISTICS
FOR THE HEALTH SCIENCES
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15 MATH 146
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3 UG CR
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Prerequisite:
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Two years of high school algebra. MPT score of 420 or above
recommended.
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Text:
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Knapp, R.G., Basic
Statistics for Nurses, 2nd Edition
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| |
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)
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ELEMENTARY
PROBABILITY AND STATISTICS I, II, III
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15 MATH 147, 148, 149
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3 UG CR ea. qtr. (May be used for the 9-credit A&S
mathematics requirement.)
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Prerequisite:
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Knowledge of high school algebra. Score of 420 or above on the
Math Placement Test recommended.
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Text:
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Moore and McCabe, Introduction to the Practice of
Statistics, 5th Edition
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15 MATH 147
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DATA: Distributions and graphs, summarizing data, normal
distribution, scatterplots, categorical data,
designing samples and experiments, probability. Aut., Sum. Qtrs
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15 MATH 148
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PROBABILITY AND INFERENCE: Sampling distributions,
probability, sample proportions and means, binomial distribution,
confidence intervals, inference for means, comparing two means. Win., Sum. Qtrs.
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15 MATH 149
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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.
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HONORS
ELEMENTARY PROBABILITY AND STATISTICS I, II, III
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15 MATH 147H, 148H, 149H
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3 UG CR ea. qtr. (May be used for the 9-credit A&S
mathematics requirement.)
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Prerequisite:
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University Honors Scholars; knowledge of high school algebra.
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Text:
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Moore and McCabe, Introduction to the Practice of
Statistics, 5th Edition
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15 MATH 147H
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Honors
version of 15 Math 147 Aut. Qtr.
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15 MATH 148H
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Honors version of 15 Math 148 Win Qtr.
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15 MATH 149H
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Honors version of 15 Math 149 Spr Qtr.
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TOPICS
IN MATHEMATICS I, II, III
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15 MATH 155, 156, 157
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3 UG CR ea. qtr. (May be used for the 9-credit A&S
mathematics requirement.)
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Prerequisite:
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Two years of high school algebra and plane geometry or the
equivalent. Score of 420 or above on Math Placement Test recommended. Courses
may be taken in any order.
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Text:
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Tannenbaum, Excursions in Modern Mathematics, 6th Edition
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15 MATH 155
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Management Science: Euler circuits, Hamiltonian
circuits, traveling salesman problems, minimum-cost spanning trees,
critical path analysis, scheduling tasks, bin packing, mixture problems,
linear programming. Aut., Sum. Qtrs.
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15 MATH 156
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Collecting and describing data; probability; statistical
inference.
Wtr.,
Sum. Qtrs.
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15 MATH 157
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Voting systems, fair division, and apportionment. Spr., Sum. Qtrs.
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HONORS TOPICS
IN MATHEMATICS I, II, III
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15 MATH 155H, 156H, 157H
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3 UG CR ea. qtr. (May be used for the 9-credit A&S mathematics
requirement.)
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Prerequisite:
|
Two years of high school algebra and plane geometry or the
equivalent. Score of 420 or above on Math Placement Test recommended. Courses
may be taken in any order.
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Text:
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Tannenbaum, Excursions in Modern Mathematics, 6th Edition |
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15 MATH 155H
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Honors version of 15 Math 155. Aut., Sum. Qtrs.
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15 MATH 156H
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Honors version of 15 Math 156. Wtr., Sum. Qtrs.
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15 MATH 157H
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Honors version of 15 Math 157. Spr., Sum. Qtrs.
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COLLEGE
ALGEBRA I, II
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15 MATH 173,174
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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.)
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Prerequisite:
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Two years
of high school algebra and plane geometry or the equivalent, such as 42-Math-101 (Elementary Algebra III.).
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Text:
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Swokowski, Algebra & Trigonometry with
Analytical Geometry (custom), 12th
edition
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15 MATH 173
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Review of basic algebra. Graphing, quadratic equations, linear
and nonlinear inequalities, modeling, functions. Pre-req: Score
of 430 or above on Math Placement Test. Aut., Wtr, Spr,
Sum. Qtrs.
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15 MATH 174
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Inverse functions; polynomial, rational, exponential, and
logarithmic functions, systems of linear equations, systems of
inequalities. Pre-req: 15 Math 173 or a score of
500 or above on the Math Placement Test.
Aut, Wtr., Spr, Sum. Qtrs.
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TRIGONOMETRY
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15 MATH 181
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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.)
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Prerequisite:
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15 MATH 174 or equivalent. Score of 530 or above on Math
Placement Test.
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Text:
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Swokowski, Algebra & Trigonometry with
Analytical Geometry (custom), 12th
edition
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| |
Right
triangle trigonometry, laws of sines and cosines,
trigonometric functions and graphs, trigonometric identities, vectors,
conic sections, polar coordinates. Aut, Spr, Sum Qtrs.
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COOPERATIVE
LEARNING IN CALCULUS 0, I, II, III, IV
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15 MATH 200, 201, 202, 203, 204
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1 UG CR ea. qtr
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Co-requisite:
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Registration in corresponding Calculus class
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Text:
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BOOK NOT REQUIRED (Text based on book from Calculus 0, I, II,
III).
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15 MATH 200
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Guided group work to complement the Calculus 0 (15 Math 250) curriculum. Aut. Qtr. only
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15 MATH 201
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Guided group work to complement the Calculus
I (15 Math 251) curriculum. Aut., Win. Qtrs.
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15 MATH 202
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Guided group work to complement the Calculus II (15 Math 252) curriculum.
Win., Spr. Qtrs.
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15 MATH 203
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Guided group work to complement the Calculus III (15 Math 253) curriculum. Spr., Sum. Qtrs.
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15 MATH 204
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Guided group work to complement the Calculus IV (15 Math 264) curriculum. Aut. Qtr. only
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FOUNDATIONS
OF APPLIED CALCULUS, FINITE MATH, APPLIED CALCULUS I, II
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15 MATH 224, 225, 226, 227
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3 UG CR ea. qtr. Either 224, 226, 227 or 225, 226, 227 can be used for the
9-credit A&S mathematics requirement.
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15 MATH 224
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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)
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Prerequisite:
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A score of 470 or better on the Math Placement Test.
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Text:
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Connally, Hughes-Hallet, Gleason, et al. Functions Modeling Change,
3rd edition (custom edition for the
University of
Cincinnati)
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15 MATH 225
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Finite Mathematics. Linear models, systems of linear equations
and matrices, matrix algebra and applications, linear programming,
non-linear models.
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Prerequisite:
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15 Math 174. Score of 530 or better
on the Math Placement Test.
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Text:
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Sullivan & Mizrahi, Finite Mathematics: An Applied Approach, 9th
edition
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15 MATH 226
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Applied Calculus I. Functions, graphs, limits, continuity,
differentiation, curve sketching, optimization. Properties of exponential
and logarithmic functions. Aut., Win., Sum. Qtrs. (Spr.,
evenings only).
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Prerequisite:
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15 Math 224. Score of 575 or better
on the Math Placement Test.
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Text:
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Hughes-Hallet/Gleason/Lock/Flath/et al. Applied Calculus, 3rd edition
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15 MATH 227
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Applied Calculus II. Antidifferentiation,
the definite integral, area, probability, functions of two variables,
partial derivatives, maxima and minima, Lagrange multipliers. Win., Spr., Sum. Qtrs. (Aut, evenings only)
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Prerequisite:
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15 Math 226.
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Text:
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Hughes-Hallet/Gleason/Lock/Flath/et al. Applied Calculus, 3rd edition |
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HONORS
FINITE MATHEMATICS & CALCULUS I, II, III
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15 MATH 225H, 226H, 227H
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3 UG CR ea. qtr. Can be used for the 9-credit A&S
mathematics requirement.
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Prerequisite:
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University Honors scholars and students in Honors Plus
Program.
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15 MATH 225H
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Topics from Finite Math, such as solving systems of linear
equations, matrices, linear programming. Aut.
Qtr.
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Text:
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Sullivan & Mizrahi, Finite Mathematics: An Applied Approach, 9th edition |
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15 MATH 226H
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Honors version of 15 MATH 226. Win. Qtr.
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Text:
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Hughes-Hallet/Gleason/Lock/Flath/et al. Applied Calculus, 3rd edition |
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15 MATH 227H
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Honors version of 15 MATH 227. Spr. Qtr.
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Text:
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Hughes-Hallet/Gleason/Lock/Flath/et al. Applied Calculus, 3rd edition |
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ALGEBRA
AND FINITE MATH, CONCEPTS OF CALCULUS
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15 MATH 228, 229
THESE COURSES HAVE BEEN DISCONTINUED AS OF WINTER QUARTER 2007 |
3 UG CR ea qtr
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Prerequisite:
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Math 174 or Math 224 or a score of 530 or better on the
Mathematics Placement Exam.
College
of
Business students
only.
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Text:
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Waner Costenoble,
Finite Mathematics and Applied
Calculus, 3rd edition
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15 MATH 228
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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.
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15 MATH 229
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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.
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CALCULUS
0
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15 MATH 250
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5 UG CR
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Prerequisite:
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A score of 550 or better on the Math Placement Test.
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Text:
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Faires, Pre-Calculus,
4th edition
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| |
For students who need
more preparation before entering 15 Math 251.
Aut.,
Win., Sum. Qtrs.
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CALCULUS
I, II, III
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15 MATH 251, 252, 253
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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.
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Prerequisite:
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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.
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Text:
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Stewart, Calculus:
Concepts and Contexts, 3rd Edition
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15 MATH 251
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Functions, limits and continuity, derivatives,
applications of the derivative, antiderivatives. Aut.,
Win., Spr. Qtrs. (5 CR) (Eves in
Sum.)
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15 MATH 252
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The integral, inverse functions, techniques of integration,
applications of the integral. Win., Spr, Sum. Qtrs. (Eves in Aut.)
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15 MATH 253
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Sequences and series, vectors, lines and planes, vector-valued
functions. Aut., Spr., Sum. Qtrs. (Eves in
Win.)
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HONORS
CALCULUS I, II, III
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|
15 MATH 251H, 252H, 253H
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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.
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Text:
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Stewart, Calculus:
Concepts and Contexts, 3rd Edition
|
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15 MATH 251H
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Honors version of 15 MATH 251. Aut. Qtr.
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|
15 MATH 252H
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Honors version of 15 MATH 252. Win. Qtr.
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15 MATH 253H
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Honors version of 15 MATH 253. Spr.
Qtr.
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CALCULUS
II, III LABS
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15 MATH 256, 257, (258)
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1 UG CR ea. qtr
|
|
15 MATH 256
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Calc II Lab to accompany Calculus II
(Co-requisite: Calculus 252.)
Win., Spr., Sum. Qtrs.
(Eves in Aut.)
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Text: |
Hollis, Calc Lab with Mathematica
– Single Variable, 3rd edition |
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15 MATH 257
|
Calc III Lab to
accompany Calculus III (Co-requisite: Calculus 253.)
Aut.,
Spr., Sum. Qtrs. (Eves in Win.)
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|
Text: |
Hollis, Calc Lab with Mathematica – Multi-Variable,
3rd edition |
|
CALCULUS
IV
|
|
15 MATH 264
|
5 UG CR ea. qtr
|
|
Pre-requisite:
|
Calculus III (15 MATH 253).
|
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Text:
|
Stewart, Calculus:
Concepts and Contexts, 3rd Edition
|
| |
Partial derivatives, multiple integrals, calculus of vector
fields.
Aut., Win., Spr. Qtrs.
|
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HONORS
CALCULUS IV
|
|
15 MATH 264H
|
5 UG CR ea. qtr
|
|
Pre-requisite:
|
Calculus III (15 MATH 253) and Honors
Scholars status.
|
| Text: |
Stewart, Calculus: Concepts and Contexts, 3rd Edition |
| |
Honors version of 15 Math 264. Aut. Qtr.
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DIFFERENTIAL
EQUATIONS
|
|
15 MATH 273
|
5 UG CR
|
|
Prerequisite:
|
Calculus III (15 MATH 253).
|
|
Text:
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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.
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|
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:
|
Lamon, Teaching
Fractions & Ratios for Understanding, 2nd edition
|
| |
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 math education in grades 5 – 12. Spr. Qtr.
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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:
|
Bunt, The Historical
Roots of Elementary Mathematics, (1988)
|
| |
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 (Applied
Calculus II)
|
|
Text:
|
No Book Needed at this time
|
| |
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 (Applied Calculus II) and 15 Math 303 (Algebra for
Teachers) or permission of instructor.
|
|
Text:
|
No Book Needed at this time
|
| |
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
(custom), 1st 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, Differential Equations and Their
Applications, 4th edition
|
| |
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, et al, A Transition to Advanced Mathematics, 6th Edition
|
| |
Logic, proofs, set
theory, relations, functions, and 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, 8th
Edition
|
|
15 MATH 361
|
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
|
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 software package may be used. Win., Spr., Sum. Qtrs.
|
|
15 MATH 363
|
More linear
regression, multiple linear regression, analysis of variance, experimental
design, reliability, and quality control. SAS software package may be used.
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:
|
Montgomery, Runger, & Hubele, Engineering Statistics, 2007
|
| |
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 264)
and Differential Equations (15 MATH 273).
|
|
Text:
|
Haberman, Elementary Applied Partial Differential Equations, 4th edition
|
| |
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:
|
Dunham, Journey Through Genius, (1991)
|
|
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
|
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15 MATH 406, 407
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3 UG CR ea. qtr.
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| Prerequisite: |
Intro to Abstract Math (15 MATH 357) |
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Text: |
No Book Needed at this time |
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15 MATH 406
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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.
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Prerequisite:
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Intro to Geometry I (15 MATH 406) |
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Text:
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No Book Needed at this time |
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15 MATH 407
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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.
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INTRODUCTION TO
ANALYSIS I, II
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15 MATH 408, 409
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3 UG CR ea. qtr.
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15 MATH 408
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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.
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Prerequisite:
|
Introduction to
Abstract Math (15 MATH 357)
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Text:
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Wright, duplicated
notes (see http://math.uc.edu/408)
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15 MATH 409
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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.
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Prerequisite:
|
Introduction to Analysis I (15 MATH 408)
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Text:
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Wright, duplicated
notes (see http://math.uc.edu/409)
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DISCRETE MATH &
ITS APPLICATIONS
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15 MATH 410
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3 UG CR Credits may not be applied
toward a degree in mathematics.
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Prerequisite:
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Calculus III (15 MATH
253) and Probability & Stats I (15 MATH 361)
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Text:
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Rosen, Discrete Math & Its Applications,
6th Edition
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Logic, proofs,
induction, relations, graphs, and trees. Aut., Sum. Qtr.
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UNDERGRADUATE
INTERNSHIP IN MATHEMATICAL SCIENCES
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15 MATH 498
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1-6 UG CR
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Prerequisite:
|
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.
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Text:
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NO BOOK NEEDED
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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.
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SENIOR CAPSTONE
EXPERIENCE IN MATHEMATICAL SCIENCES
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15 MATH 501
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1 UG CR
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Prerequisite:
|
Senior standing in
mathematics.
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Text:
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NO BOOK NEEDED
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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.
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ADVANCED
CALCULUS I, II, III
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15 MATH 504, 505, 506
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3 UG or GR CR ea. qtr.
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Prerequisite:
|
Calculus IV (15 MATH 264), Introduction to
Ordinary Differential Equations (15 MATH 355), and Introduction to Abstract
Mathematics (15 MATH 357).
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Text:
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Rosenlicht, Introduction to Analysis, (1986)
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15 MATH 504
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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.
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15 MATH 505
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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.
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15 MATH 506
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Uniform convergence for sequences and series of functions, equi-continuous families of functions, the Stone-Weierstrass theorem, functions of several variables. Spr. Qtr.
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ABSTRACT
ALGEBRA I, II, III
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15 MATH 511, 512, 513
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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).
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Text:
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Lang, Linear Algebra, 3rd Edition. (Book used in 15 MATH 511 only)
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15 MATH 511
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Advanced Linear Algebra: Abstract vector spaces,
determinants, eigenvalues and eigenvectors,
algebra of linear transformations, canonical forms including triangular,
Jordan and
rational forms.
Aut.
Qtr.
|
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15 MATH 512
|
Definition and basic properties of groups, subgroups,
permutation groups, direct products, isomorphisms,
homomorphisms, normal subgroups and factor
groups. Win. Qtr.
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15 MATH 513
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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.
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NUMERICAL
ANALYSIS I, II, III
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|
15 MATH 514, 515, 516
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3 UG or GR CR ea. qtr.
|
|
Prerequisite:
|
Calculus IV (15 MATH 264); 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.
|
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Text:
|
Atkinson, An Introduction to Numerical Analysis,
2nd Edition
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15 MATH 514
|
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.
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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.
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APPLIED
MATHEMATICS PRACTICUM
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|
15 MATH 517, 518, 519
|
3 UG or GR CR ea. qtr.
|
|
Prerequisite:
|
Calculus IV (15 MATH 264), Differential Equations (15 MATH
273), and computer programming experience.
|
|
Text:
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TBA
|
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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.
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15 MATH 518
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A continuation of 15
MATH 517.
|
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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 264) and Probability and Statistics I (15
MATH 361).
|
|
Text:
|
Hogg, McKean, and
Craig, Introduction to Mathematical
Statistics, 6th Edition.
|
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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, bootstrap methods .
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 264);
Linear Algebra II (15 MATH 352)
|
|
Text:
|
No Book Needed at this time
|
|
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 (el | |
