University of Dayton
Academic Catalog 2014-15

Mathematics

Majors:

Minors:

The B.A. program in mathematics provides for a breadth of mathematical study within the context of a liberal arts degree. It may be chosen as a preparation for a professional career in business, education, law or social science. It affords the student a significant distribution of courses in the humanities and social sciences so that he or she can develop a concentration in a field other than mathematics. The student's career goals will generally suggest desirable upper level mathematics electives. For example, prospective secondary mathematics teachers should participate in the licensure program and elect courses such as MTH 370, MTH 395, and MTH 466. Students with an interest in business, law, or social science should complete the probability and statistics sequence MTH 411-MTH 412.

The B.S. program in mathematics provides a foundation for students who wish to pursue graduate studies in any area of the mathematical sciences, to enter the actuarial profession, or to enter careers where mathematics is used in an engineering or science setting. A preparation for graduate programs in a mathematical science should include electives such as MTH 342, MTH 404and MTH 471. Those planning on pursuing an actuarial career should take the actuarial science minor described below. To prepare for using mathematics in an applied context, some useful elective courses are MTH 403, MTH 404, and the MTH 411-MTH 412 sequence. All students pursuing a bachelor of science in mathematics are required to complete a minor in another subject.

The B.S. program in applied mathematical economics provides a foundation in economics, mathematics and statistics needed for graduate study in economics or applied statistics, or for research and technical careers in business or government service. This degree is offered jointly by the Department of Mathematics and the Department of Economics and Finance in the School of Business Administration.

The basic courses are offered every term:

MTH 168Analytic Geometry & Calculus I4
MTH 169Analytic Geometry & Calculus II4
MTH 218Analytic Geometry & Calculus III4
MTH 219Applied Differential Equations3
MTH 308Foundations & Discrete Mathematics3
MTH 310Linear Algebra & Matrices3

Most majors will take MTH 218 and MTH 308 in the same term.

The required core courses are offered at least once a year:

MTH 330Intermediate Analysis3
MTH 361Introduction to Abstract Algebra3
MTH 411Probability & Statistics I3
MTH 430Real Analysis3

However, most of the other upper-level electives for the major are offered only once every two years; thus careful planning for a student's upper-level electives should be done in consultation with the advisor. In addition, the symbolic logic course, PHL 302, is a recommended Common Academic Program course for all mathematics majors.

A minor in mathematics consists of 12 semester hours (300-400 level).

A minor in actuarial science is offered through the Department of Mathematics. This consists of courses in calculus, statistics, theory of interest, economics, and finance, and is designed to prepare the student to take the actuarial examinations in probability and financial mathematics.

Faculty

Joe D. Mashburn, Chairperson
Distinguished Service Professor: Peterson
Professors Emeriti: Back, Friel, Gantner, Kauflin, McCloskey, Mushenheim, Rice, Schleppi, Shaughnessy, R. Steinlage, Strange
Professors: Abueida, Diestelkamp, Eloe, Higgins, Islam, Mashburn, Raffoul
Associate Professors: Busch, Driskell, Gorton, Hovey, Krakowski, Liu, Qumsiyeh, Usman
Assistant Professors: Brown, Kublik, Ren, Yengulalp
Lecturers: Harrison, Ober, Saintignon, Simon, L. Steinlage
 

Bachelor of Arts with a major in Mathematics (mth) Minimum 124 Hours

Common Academic Program (CAP)
*credit hours will vary depending on courses selected
First-Year Humanities Commons 112
West and the World
Introduction to Religious and Theological Studies
Intro To Philosophy
Writing Seminar I 2
Second-Year Writing Seminar 30-3
Writing Seminar II
Oral Communication3
Principles of Oral Communication
Mathematics3
Social Science3
Arts3
Natural Sciences 47
Crossing Boundariesvariable credit
Faith Traditions
Practical Ethical Action
Inquiry
Integrative
Advanced Studyvariable credit
Philosophy and/or Religious Studies
Historical Studies
Diversity and Social Justice3
Major Capstone0-3

1

Completed with ASI 110 and ASI 120.

2

Or ENG 100A and ENG 100B, orENG 200H, by placement.

3

Completed with ENG 200H or ASI 120.

4

Must include two different disciplines and accompanying lab.





Liberal Studies Curriculum
Creative and Performing Arts (May include CAP Arts)3
L2 Proficiency (Proficiency in a language other than English)0-11
Literature (May include CAP Components)3
Natural Sciences (Satisfies CAP Natural Science)11
Social Sciences (Includes CAP Social Science)12

Major Requirements36
MTH 168Analytic Geometry & Calculus I (Satisfies CAP Mathematics)4
MTH 169Analytic Geometry & Calculus II4
MTH 218Analytic Geometry & Calculus III4
MTH 308Foundations & Discrete Mathematics3
MTH 310Linear Algebra & Matrices3
MTH 330Intermediate Analysis3
MTH 361Introduction to Abstract Algebra3
MTH 411Probability & Statistics I3
MTH 480Math Capstone (Satisfies CAP Major Capstone)3
Select two MTH courses (300/400 level)6

Breadth
ASI 150Introduction to the University Experience1
Total Hours to total at least124

 

Bachelor of Science with a major in Applied Mathematical Economics (mte) Minimum 120 Hours

Common Academic Program (CAP)
*credit hours will vary depending on courses selected
First-Year Humanities Commons 112
West and the World
Introduction to Religious and Theological Studies
Intro To Philosophy
Writing Seminar I 2
Second-Year Writing Seminar 30-3
Writing Seminar II
Oral Communication3
Principles of Oral Communication
Mathematics3
Social Science3
Arts3
Natural Sciences 47
Crossing Boundariesvariable credit
Faith Traditions
Practical Ethical Action
Inquiry
Integrative
Advanced Studyvariable credit
Philosophy and/or Religious Studies
Historical Studies
Diversity and Social Justice3
Major Capstone0-3

1

Completed with ASI 110 and ASI 120.

2

Or ENG 100A and ENG 100B, orENG 200H, by placement.

3

Completed with ENG 200H or ASI 120.

4

Must include two different disciplines and accompanying lab.





Science Breadth Requirements
Satisfies CAP Natural Science
CPS 150Algorithms & Programming I4
CPS 151Algorithms & Programming II4
Select one natural sciences group from:8
BIO 151
  & 151L
  & BIO 152
  & BIO 152L
Concepts of Biology I: Cell & Molecular Biology
   and Concepts of Biology Laboratory: Cell & Molecular Biology
   and Concepts of Biology II: Evolution & Ecology
   and Concepts of Biology Laboratory II: Evolution & Ecology
CHM 123
  & 123L
  & CHM 124
  & CHM 124L
General Chemistry
   and General Chemistry Laboratory
   and General Chemistry
   and General Chemistry Laboratory
GEO 115
  & 115L
  & GEO 116
  & GEO 116L
Physical Geology
   and Physical Geology Laboratory
   and Geological History of the Earth
   and Geological History of the Earth Laboratory
PHY 206
  & PHY 207
  & PHY 210L
  & PHY 211L
General Physics I - Mechanics
   and General Physics II - Electricity & Magnetism
   and General Physics Laboratory
   and General Physics Laboratory II

Major Requirements48
Mathematics
MTH 168Analytic Geometry & Calculus I (Satisfies CAP Mathematics)4
MTH 169Analytic Geometry & Calculus II4
MTH 218Analytic Geometry & Calculus III4
MTH 308Foundations & Discrete Mathematics3
MTH 310Linear Algebra & Matrices3
MTH 330Intermediate Analysis3
MTH 411Probability & Statistics I3
MTH 412Probability & Statistics II3
MTH 480Math Capstone (Satisfies CAP Major Capstone)3
Economics
ECO 203Principles of Microeconomics (Satisfies CAP Crossing Boundaries: Inquiry)3
ECO 204Principles of Macroeconomics (Satisfies CAP Crossing Boundaries: Inquiry)3
ECO 346Intermediate Microeconomic Analysis3
ECO 347Intermediate Macroeconomic Analysis3
ECO 441Econometrics3
Select one ECO course (300/400 level)3

Breadth
ASI 150Introduction to the University Experience1
Social and Behavioral Sciences (Includes CAP Social Science)6
Total Hours to total at least120

 

Bachelor of Science with a major in Mathematics (mth) Minimum 120 Hours

Common Academic Program (CAP)
*credit hours will vary depending on courses selected
First-Year Humanities Commons 112
West and the World
Introduction to Religious and Theological Studies
Intro To Philosophy
Writing Seminar I 2
Second-Year Writing Seminar 30-3
Writing Seminar II
Oral Communication3
Principles of Oral Communication
Mathematics3
Social Science3
Arts3
Natural Sciences 47
Crossing Boundariesvariable credit
Faith Traditions
Practical Ethical Action
Inquiry
Integrative
Advanced Studyvariable credit
Philosophy and/or Religious Studies
Historical Studies
Diversity and Social Justice3
Major Capstone0-3

1

Completed with ASI 110 and ASI 120.

2

Or ENG 100A and ENG 100B, orENG 200H, by placement.

3

Completed with ENG 200H or ASI 120.

4

Must include two different disciplines and accompanying lab.





Science Breadth Requirements
Computer Science (CPS 150 applies to CAP Natural Sciences)3-4
Computer Programming for Engineering & Science
Algorithms & Programming I
Select one natural sciences group from: (Applies to CAP Natural Science)8
BIO 151
  & 151L
  & BIO 152
  & BIO 152L
Concepts of Biology I: Cell & Molecular Biology
   and Concepts of Biology Laboratory: Cell & Molecular Biology
   and Concepts of Biology II: Evolution & Ecology
   and Concepts of Biology Laboratory II: Evolution & Ecology
CHM 123
  & 123L
  & CHM 124
  & CHM 124L
General Chemistry
   and General Chemistry Laboratory
   and General Chemistry
   and General Chemistry Laboratory
GEO 115
  & 115L
  & GEO 116
  & GEO 116L
Physical Geology
   and Physical Geology Laboratory
   and Geological History of the Earth
   and Geological History of the Earth Laboratory
PHY 206
  & PHY 207
  & PHY 210L
  & PHY 211L
General Physics I - Mechanics
   and General Physics II - Electricity & Magnetism
   and General Physics Laboratory
   and General Physics Laboratory II
Select two courses acceptable for science majors6

Major Requirements45
MTH 168Analytic Geometry & Calculus I (Satisfies CAP Mathematics)4
MTH 169Analytic Geometry & Calculus II4
MTH 218Analytic Geometry & Calculus III4
MTH 219Applied Differential Equations3
MTH 308Foundations & Discrete Mathematics3
MTH 310Linear Algebra & Matrices3
MTH 330Intermediate Analysis3
MTH 361Introduction to Abstract Algebra3
MTH 430Real Analysis3
MTH 480Math Capstone (Satisfies CAP Major Capstone)3
Select four MTH courses (300/400 level) 112

Breadth
ASI 150Introduction to the University Experience1
Social and Behavioral Sciences (Includes CAP Social Science)6
Total Hours to total at least120

1

Departmental approval required.


Minor in Actuarial Science (acs)

The Minor in Actuarial Science is designed to prepare students to pass the P and FM actuarial tests. It is also designed to supply students with VEE (Validation by Educational Experience) credit in economics, corporate finance, and applied statistics.

The minor contains eight courses in mathematics for a total of 22 semester hours. One of these is a course in the theory of interest and one is a seminar which prepares students to take the P test. Mathematics majors will take all but two of the mathematics requirements for the minor as part of their major requirements.

The minor also contains eight courses in accounting, economics, and finance for a total of twenty-four semester hours. Economics and finance majors will take all of these courses as part of their major requirements. They will be able to substitute two of the mathematics courses for those that they are required to take for their major.

A total of 46 semester hours are required for the minor.

Actuarial Science
ACC 207Introduction to Financial Accounting3
ECO 203Principles of Microeconomics 13
ECO 204Principles of Macroeconomics 13
ECO 410Bus&Eco Forecasting 23
FIN 301Introduction to Financial Management 33
FIN 360Investments3
FIN 470Fixed Income Securities3
FIN 480Options & Futures Markets3
MTH 168Analytic Geometry & Calculus I 4
MTH 169Analytic Geometry & Calculus II4
MTH 218Analytic Geometry & Calculus III4
MTH 229Theory of Interest3
MTH 328Actuarial Probability Seminar1
MTH 411Probability & Statistics I3
MTH 412Probability & Statistics II3
Total Hours46

1

ECO 203 and  ECO 204 together qualify for VEE Economics credit in Economics.

2

VEE credit in Applied Statistics.

3

This course counts as VEE credit in Corporate Finance.

 

Minor in Mathematics (mth)

Mathematics
Select four MTH courses (300/400 level)12
Total Hours12
  • Bachelor of Arts, Mathematics
  • Bachelor of Science, Applied Mathematical Economics
  • Bachelor of Science, Mathematics

Bachelor of Arts, Mathematics

First Year
FallHoursSpringHours
ASI 1501MTH 1694
MTH 1684Natural Science w/lab4
Natural Science w/lab4REL 103, PHL 103, or HST 103 (satisifes CAP Humanities)3
ENG 100 (satisfies CAP Writing Seminiar)3REL 103, PHL 103, or HST 103 (satisifes CAP Humanities)3
REL 103, PHL 103, or HST 103 (satisfies CAP Humanities)3Social Science (CAP)3
 15 17
Second Year
FallHoursSpringHours
MTH 2184MTH 3103
MTH 3083Literature3
CMM 100 (satisifes CAP Communication)3Social Science3
ENG 2003Language4
Natural Science3Arts3
 16 16
Third Year
FallHoursSpringHours
MTH 4113MTH 3613
MTH elective3MTH elective3
Language4Language3
Social Science3Inquiry3
Adv PHL/REL (PEA/FT)3Integrative3
 16 15
Fourth Year
FallHoursSpringHours
MTH 3303MTH 480 (capstone)3
Social Science3MTH elective3
Adv PHL/REL (PEA/FT)3Diversity and Social Justics3
Adv HST3General elective3
General Elective3General Elective3
 15 15
Total credit hours: 125

Bachelor of Science, Applied mathematical economics

First Year
FallHoursSpringHours
ASI 1501MTH 1694
MTH 1684ECO 2043
ECO 2033REL 103, PHL 103, or HST 103 (satisfies CAP Humanities)3
ENG 100 (satisfies CAP Writing Seminar)3REL 103, PHL 103, or HST 103 (satisfies CAP Humanities)3
Natural Science w. Lab4Natural Science w/Lab4
 15 17
Second Year
FallHoursSpringHours
MTH 2184MTH 3103
MTH 3083ECO 3473
ECO 3463CMM 100 (satisfies CAP Communication)3
ENG 2003Adv PHL/REL (PEA/FT)3
REL 103, PHL 103, or HST 103 (satisfies CAP Humanities)3Social Science (CAP)3
 16 15
Third Year
FallHoursSpringHours
MTH 4113MTH 4123
CPS 1504CPS 1514
Inquiry3Integrative3
Adv PHL/REL/ (PEA/FT)3General Elective3
Arts3General Elective3
 16 16
Fourth Year
FallHoursSpringHours
MTH 3303MTH 480 (capstone)3
ECO 4413ECO elective3
Adv HST3Diversity and Social Justice3
General Elective3General Elective (optional)3
General Elective1General Elective (optional)3
General Elective3 
 16 15
Total credit hours: 126

Bachelor of Science, Mathematics

First Year
FallHoursSpringHours
ASI 1501MTH 1694
MTH 1684REL 103, PHL 103, or HST 1033
ENG 1003REL 103, PHL 103, or HST 1033
REL 103, PHL 103, or HST 1033Natural Science w/lab4
Natural Science w/ lab4Social Science (CAP)3
 15 17
Second Year
FallHoursSpringHours
MTH 2184MTH 2193
MTH 3083Natural Science3
ENG 2003MTH 3103
CMM 1003Arts3
Natural Science3Social Science (CAP)3
 16 15
Third Year
FallHoursSpringHours
MTH 3303MTH 3613
MTH elective3MTH elective3
CPS 132 or 1503-4Inquiry3
Minor elective3Integrative3
Adv PHL/REL (PEA/FT)3Minor elective3
 15-16 15
Fourth Year
FallHoursSpringHours
MTH 4303MTH 4803
MTH elective3MTH elective3
Adv PHL/REL (PEA/FT)3Minor elective3
Minor elective3Diversity and Social Justice3
Minor elective3Adv HST3
 15 15
Total credit hours: 123-124

Courses

MTH 102. Fundamentals of Math. 3 Hours

Sets, functions and graphs, exponents, polynomials and algebraic equations, systems of equations. Prerequisite(s): One year of high school algebra.

MTH 114. Contemporary Mathematics. 3 Hours

Study of contemporary mathematical topics and their applications. Topics may include management science, statistics, social choice, size and shape, and computer mathematics. Prerequisite(s): Two years of high school algebra.

MTH 116. Precalculus Math. 4 Hours

Review of topics from algebra and trigonometry including polynomials, functions and graphs, exponential and logarithmic functions, trigonometric functions and identities. Prerequisite(s): Two years of high school algebra.

MTH 128. Finite Mathematics. 3 Hours

Topics from mathematics used in business including systems of equations, inequalities, matrix algebra, linear programming and logarithms; applications to compound interest, annuities and other finance problems. Prerequisite(s): MTH 102 or sufficient college preparatory mathematics.

MTH 129. Calculus for Business. 3 Hours

Topics from differential and integral calculus used in business; applications to optimizing financial functions, marginal functions in economics, and consumer or producer surplus. Prerequisite(s): MTH 128 or sufficient college preparatory mathematics.

MTH 137. Calculus I with Review. 4 Hours

Introduction to the differential and integral calculus with an extensive review of algebra and trigonometry; differentiation and integration of algebraic and transcendental functions with applications. Prerequisite(s): Two years of high school algebra.

MTH 138. Calculus I with Review. 4 Hours

Introduction to the differential and integral calculus with an extensive review of algebra and trigonometry; differentiation and integration of algebraic and transcendental functions with applications. Prerequisite(s): MTH 137.

MTH 148. Introductory Calculus I. 3 Hours

Introduction to the differential and integral calculus; differentiation and integration of algebraic and transcendental functions with applications to the life and social sciences. Prerequisite(s): MTH 116 or equivalent.

MTH 149. Introductory Calculus II. 3 Hours

Continuation of MTH 148. Multivariable calculus, matrices, difference equations, probability, discrete and continuous random variables, and differential equations with applications to the life and social sciences. Prerequisite(s): MTH 138 or MTH 148.

MTH 168. Analytic Geometry & Calculus I. 4 Hours

Introduction to the differential and integral calculus; differentiation and integration of algebraic and transcendental functions with applications to science and engineering. Prerequisite(s): MTH 116 or equivalent.

MTH 169. Analytic Geometry & Calculus II. 4 Hours

Continuation of MTH 168. Conic sections, techniques of integration with applications to science and engineering, infinite series, indeterminate forms, Taylor's theorem. Prerequisite(s): MTH 138 or MTH 168.

MTH 169H. Analytic Geometry & Calculus II. 4 Hours

Continuation of MTH 168. Conic sections, techniques of integration with applications to science and engineering, infinite series, indeterminate forms, Taylor's theorem. Prerequisite(s): MTH 138 or MTH 168.

MTH 204. Mathematical Concepts I. 3 Hours

First course of a two-semester sequence designed for pre-service teachers. Concepts necessary for an understanding of the structure of arithmetic and its algorithms, number patterns, sets, problem solving, percent, relation and proportion, use of calculators. Prerequisite(s): One year of high school algebra; one year of high school geometry.

MTH 205. Mathematical Concepts II. 3 Hours

Continuation of MTH 204. Topics include probability, representing and interpreting data, the metric system, elementary geometry, geometric patterns, coordinate geometry, algebra and geometry, transformations, computer literacy. Prerequisite(s): MTH 204.

MTH 207. Introduction to Statistics. 3 Hours

Introduction to the concepts of statistical thinking for students whose majors do not require calculus. Methods of presenting data, including graphical methods. Using data to make decisions and draw conclusions. Basic ideas of drawing a sample and interpreting the information that it contains. Prerequisite(s): Two years of high school algebra.

MTH 214. Mathematical Concepts for Middle School Teachers. 3 Hours

Concepts necessary for an understanding of the arithmetic taught in both elementary and middle grades. Includes a study of the structure of arithmetic and its algorithms; problem solving; reasoning and proof; proportional reasoning; use of computers and calculators to solve problems. Prerequisite(s): Two years of high school algebra.

MTH 215. Algebra, Functions & Graphs. 3 Hours

Development of the algebra of various families of functions including polynomial, exponential, logarithmic, and trigonometric functions; factoring and roots; interpretation of graphs; use of calculators and data collection devices to solve problems. Prerequisite(s): MTH 214.

MTH 216. Calculus Concepts & Applications. 3 Hours

Develop conceptual understanding of basic calculus concepts; introduction to the notion of limit; rates of change; slopes and area computations; use of calculators and data collection devices to make predictions, estimations, and solve problems. Prerequisite(s): MTH 215.

MTH 218. Analytic Geometry & Calculus III. 4 Hours

Continuation of MTH 169. Solid analytic geometry, vectors and vector functions, multivariable calculus, partial derivatives, multiple integrals. Prerequisite(s): MTH 169.

MTH 219. Applied Differential Equations. 3 Hours

First order equations, linear equations with constant coefficients, systems of equations, the Laplace transform, numerical methods, applications. Prerequisite(s): MTH 218.

MTH 229. Theory of Interest. 3 Hours

Rigorous, calculus-based treatment of the Theory of Interest. Topics covered include interest, compounding, discounting, annuities, sinking funds, amortization, bonds, yield rates, and applications of these ideas and processes to problems in finance. Prerequisite(s): MTH 169.

MTH 250. Advanced Technical Mathematics. 3 Hours

Appropriate analytical techniques for students of engineering technology; topics include integration by parts, multivariable calculus, complex numbers, matrices and system of linear equations, and first and second order differential equations. Applications are appropriate for the engineering technology programs (circuits, vibrations, and heat transfer). Prerequisite(s): MTH 138 or MTH 168.

MTH 266. Discrete & Finite Mathematics for Middle School Teachers. 3 Hours

Topics in finite and discrete mathematics; linear programming; applications in finance; graph theory; mathematics of social choice; logic; use of computers and calculators to model and solve problems. Prerequisite(s): MTH 214.

MTH 270. Geometry Concepts & Applications. 3 Hours

Introduction to the geometry of two- and three-dimensional space; patterns in geometry; measurement systems; transformations and similarity; coordinate geometry; the algebra of geometry; trigonometry; use of dynamic computer software to explore geometric concepts. Prerequisite(s): MTH 214.

MTH 290. Topics in Mathematics. 1-3 Hours

Exploration of varying topics appropriate for the needs of the pre-service training of teachers of mathematics. May be repeated as topics change. Prerequisite(s): One mathematics course beyond MTH 102; permission of department chairperson and/or instructor.

MTH 295. Historical Roots of Elementary Mathematics. 3 Hours

Fundamental historical development of modern arithmetic, algebra, geometry, and number systems from early Egyptian, Babylonian, and Greek sources. Students may not receive credit for both this course and MTH 395. Prerequisite(s): MTH 214.

MTH 308. Foundations & Discrete Mathematics. 3 Hours

An introduction to proof using topics in foundational and discrete mathematics; propositional logic; number theory; sequences and recursion; set theory; relations; combinatorics; linear programming. Prerequisite(s): MTH 169.

MTH 310. Linear Algebra & Matrices. 3 Hours

Fundamental concepts of vector spaces, determinants, linear transformations, matrices, inner product spaces, and eigen-vectors. Offered each term. Prerequisite(s): MTH 218, MTH 308. (May be taken as corequisites).

MTH 328. Actuarial Probability Seminar. 1 Hour

Problem solving seminar to develop and improve skills in applied probability. This seminar will focus on actuarial applications of probability theory. Prerequisite(s): MTH 411.

MTH 329. Actuarial Finance Seminar. 1 Hour

Problem solving seminar to develop and improve skills in applied mathematical finance. This seminar will focus on integrating the mathematical presentation of the Theory of Interest to the field of finance. Prerequisite(s): FIN 470; MTH 229.

MTH 330. Intermediate Analysis. 3 Hours

Theoretical development of the calculus of a real-valued function of a real variable. Topics include the algebraic and topological properties of the real line, limits of sequences and functions, continuity, differentiability, and integration. Prerequisite(s): MTH 310.

MTH 342. Set Theory. 3 Hours

Elementary set theory including relations, functions, indexed families, denumerable and nondenumerable sets, cardinal and ordinal arithmetic, Zorn's Lemma, the well-ordering principle and transfinite induction. Prerequisite(s): MTH 218, MTH 308.

MTH 343. Mathematics for Electrical & Computer Engineers. 3 Hours

Linear algebra and matrices, complex variables, mathematical transforms and their inter-relations. Focus on mathematical theories as well as applications and an extensive use of MATLAB. Prerequisite(s): MTH 219.

MTH 361. Introduction to Abstract Algebra. 3 Hours

Fundamental concepts of groups, rings, integral domains and fields. Prerequisite(s): MTH 218, MTH 308.

MTH 367. Statistical Methods I. 3 Hours

Probability distributions including binomial, hypergeometric, Poisson, and normal. Estimation of population mean and standard deviation: Confidence intervals and tests of hypotheses using t-, Chi-square, and F-statistics. Mathematics majors enroll in MTH 411 instead of MTH 367. Prerequisite(s): MTH 149 or MTH 169.

MTH 368. Statistical Methods II. 3 Hours

Distribution-free methods including rank tests, sign tests, and Kolmogorov-Smirnov test. Method of least squares, correlation, linear regression, analysis of variance. Design of experiments and computer applications. Mathematics majors enroll in MTH 412 instead of 368. Prerequisite(s): MTH 367.

MTH 370. Introduction to Higher Geometry. 3 Hours

Projective, affine, and hyperbolic geometries using synthetic and/or analytic techniques. Prerequisite(s): MTH 218, MTH 308.

MTH 376. Number Theory. 3 Hours

Topics include Diophantine equations, Chinese Remainder theorem, Mobius inversion formula, quadratic residues and the Law of Quadratic Reciprocity, Gaussian integers, and integral quaternions. Prerequisite(s): MTH 218, MTH 308.

MTH 395. Development of Mathematical Ideas. 3 Hours

The evolution of mathematical ideas and techniques from ancient times to the present with emphasis on the Greek era. Famous people and famous problems. Chronological outline of mathematics in each of its branches along with applications. Prerequisite(s): MTH 218, MTH 308.

MTH 403. Boundary Value Problems. 3 Hours

Introduction to the Sturm-Liouville problem. Fourier trigonometric series, Fourier integrals, Bessel functions, and Legendre polynomials. The heat equation, wave equation, and Laplace's equation with applications. Solutions by the product method. Prerequisite(s): MTH 219, MTH 310.

MTH 404. Complex Variables. 3 Hours

Functions of a complex variable, conformal mapping, integration in the complex plane. Laurent series and residue theory. Prerequisite(s): MTH 219.

MTH 411. Probability & Statistics I. 3 Hours

Mathematical probability, random variables, Bayes' Theorem, Chebyshev's Inequality, Binomial, Poisson, and Normal probability laws, moment generating functions, limit theorems, descriptive statistics, large sample statistical inference. MTH 308 is recommended as preparation for this course. Prerequisite(s): MTH 218.

MTH 411H. Probability & Statistics I. 3 Hours

Mathematical probability, random variables, Bayes' Theorem, Chebyshev's Inequality, Binomial, Poisson, and Normal probability laws, moment generating functions, limit theorems, descriptive statistics, large sample statistical inference. MTH 308 is recommended as preparation for this course. Prerequisite(s): MTH 218.

MTH 412. Probability & Statistics II. 3 Hours

Multivariate distributions, transformations of random variables, sampling distribution theory, estimation of parameters including maximum likelihood, confidence intervals, the Neyman-Pearson lemma, tests of hypotheses, likelihood ratio tests. Prerequisite(s): MTH 411.

MTH 430. Real Analysis. 3 Hours

Continuation of MTH 330. Topics include the theory of convergence of sequences and series of functions in the context of metric spaces, uniform continuity, uniform convergence, and integration. Prerequisite(s): MTH 330.

MTH 435. Advanced Multivariate Calculus. 3 Hours

Topics include directional derivatives, chain rule, Lagrange multipliers, Taylor's formula, the mean value theorem, inverse mapping theorem, implicit function theorem, integration, Fubini's theorem, change of variables, line integrals, Green's theorem and Stoke's theorem. Prerequisite(s): MTH 310.

MTH 440. Introduction to Mathematical Modeling. 3 Hours

Introduction to the use of mathematical techniques and results in constructing and modifying models designed to solve problems encountered in everyday life. Computer simulation and limitations thereof, dimensional analysis, scaling and approximations at various levels are discussed. Prerequisite(s): MTH 219, MTH 310.

MTH 441. Mathematics Clinic. 1 Hour

Student teams will be responsible for the development and/or modification and testing of a mathematical model designed for a particular purpose. Faculty guidance. Prerequisite(s): MTH 440; permission of department chairperson.

MTH 445. Special Topics in Mathematics. 1-3 Hours

Lectures in specialized areas such as abstract algebra, applied mathematics, complex variables, differential forms, functional analysis, Galois theory, game theory, general topology, normed linear spaces, probability theory, real variables, topological groups. May be taken more than once. Prerequisite(s): Permission of department chairperson.

MTH 458. Mathematical Models in Finance. 3 Hours

Mathematical models in finance which include discrete and continuous models for stock price, interest rate model, bond pricing model, and option pricing model. Quantitative methods are introduced and employed. The methods include Black-Scholes formula, Monte-Carlo simulation, and binomial tree. Markowitz's optimal portfolio selection method is introduced and employed. Prerequisite(s): MTH 310.

MTH 465. Linear Algebra. 3 Hours

Vector spaces, linear transformations and matrices, determinants, inner product spaces, invariant direct-sum decomposition and the Jordan canonical form. Prerequisite(s): MTH 310.

MTH 466. Graph Theory & Combinatiorics. 3 Hours

Graphs as algebraic structures; Eulerian, Hamiltonian, complete, connected and planar graphs. Applications include scheduling and routing problems. Discussion of algorithms for optimal or near-optimal solutions. Combinatorial topics could include generating functions, recurrence relations, Polya's theorem and Ramsey Theory. Prerequisite(s): MTH 308 or MTH 310.

MTH 467. Combinatorial Design Theory. 3 Hours

Topic include discussion of Latin squares, mutually orthogonal Latin squares, orthogonal and perpendicular arrays, Steiner triple systems, block designs, difference sets, and finite geometries. Prerequisite(s): MTH 308.

MTH 471. Topology. 3 Hours

Introduction to topological spaces and continuous functions including a study of separation and countability axioms and elementary properties of metric spaces, connected spaces, and compact spaces. Prerequisite(s): MTH 308.

MTH 477H. Honors Thesis. 3 Hours

First of two courses leading to the selection, design, investigation, and completion of an independent, original Honors Thesis project under the guidance of a faculty research advisor. Restricted to students in the University Honors Program with permission of the program director and department chairperson. Students pursuing an interdisciplinary thesis topic may register for three semester hours each in two separate disciplines in consultation with the department chairpersons. Prerequisite(s): Approval of University Honors Program.

MTH 478H. Honors Thesis. 3 Hours

Second of two courses leading to the selection, design, investigation, and completion of an independent, original Honors Thesis project under the guidance of a faculty research advisor. Restricted to students in the University Honors Program with permission of the program director and department chairperson. Students pursuing an interdisciplinary thesis topic may register for three semester hours each in two separate disciplines in consultation with the department chairpersons. Prerequisite(s): Approved 477; approval of University Honors Program.

MTH 480. Math Capstone. 3 Hours

No description available.

MTH 490. Readings in Mathematics. 1-3 Hours

Individual study in specialized areas carried out under the supervision of a staff member. May be taken more than once. Prerequisite(s): Permission of department chairperson.