Undergraduate Course Catalog

Mathematical Sciences

J. Lorch, Chairperson 

By focusing on strong analytical and quantitative skills, the mathematical sciences programs prepare students for professional positions in a variety of areas. The department offers majors in actuarial science, mathematical sciences, and mathematics teaching. In conjunction with the Department of Economics, the department offers a major in mathematical economics. For information on the major in mathematical economics, see Interdepartmental Programs. The department minor in mathematics is open only to non-departmental majors. The minor in foundations of business for actuarial science and mathematics majors is open only to departmental majors. 

The major in actuarial science provides students with the mathematics and business education necessary to enter the actuarial profession and prepares students for the professional actuarial exams. Actuaries apply the theory of probability and statistics along with the principles of finance to analyze and solve problems in insurance, pension plans, social security issues, and related fields.

The mathematics teaching major satisfies state licensure requirements for students preparing to teach mathematics in junior high/middle school and high school. Specializations for this major are middle school and secondary school. Elementary education majors may choose mathematics as their area of concentration. Elementary education majors may also earn additional licensure to teach mathematics in junior high/middle school.

The mathematical sciences major offers students options for specialization in two areas: mathematics and applied mathematics. These programs prepare students for professional positions in business, industry, and government, as well as graduate work in mathematics or related fields, including engineering, law, or medicine.

Students wishing to declare two majors within the Department of Mathematical Sciences may do so provided that they have at least 20 semester hours of credit that is counted toward the second major not also being used as credit toward the first major. 

Unless otherwise noted, all students enrolling in courses in the Department of Mathematical Sciences are expected to have completed at least three years of college preparatory mathematics in high school, including two years of algebra and one year of geometry. To begin all programs (except the concentration in mathematics), it is expected that students will have completed high school mathematics courses equivalent to the prerequisite for MATH 165.

For majors or minors in the Department of Mathematical Sciences, a grade of C- or better must be earned in each course serving as a prerequisite for other courses applied to meet program requirements. For graduation, a grade-point average of at least 2.5 is required in a major or minor program. 


MAJOR IN ACTUARIAL SCIENCE, 59-60 hours

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MATH













RMI

165
166
215
217
251
259
267
320
321
351
452
457
458   
498
270

Calculus 1
Calculus 2
Discrete Systems
Linear Algebra
Intro to Mathematics of Financ
Intro to Mathematical Software
Calculus 3
Probability
Mathematical Statistics
Mathematics of Finance
Life Contingencies 1
Actuarial Models 1
Actuarial Models 2
Senior Seminar
Principles of Risk Mgt & Ins

4
4
4
4
2
3
4
4
4
4
4
4
3
2
3

6-7 hours from

CS  
MATH   
   



RMI

120
355
428
453
454
459 
371

Computer Science 1 (4)
Topics in Actuarial Science (1-6)
Regression Time Series Models (3)
Life Contingencies 2 (4)
Mathematics of Investments (3)
Models in Financial Economics (3)
Life & Health Insurance (3)

 

or as approved

6-7




59-60 hrs
Students may earn up to 6 credits for MATH 355, but only 4 credits will apply toward the actuarial science major. The following additional courses are strongly recommended, as they satisfy the “Validation by Educational Experience” requirements of the actuarial societies: ACC 201, ECON 201, ECON 202, MATH 428 or ECON 424, FIN 300 and one from MATH 454 or FIN 310. Other electives from the graduate actuarial science, graduate statistics, business, and economics programs are encouraged. Students are encouraged to take CS 120 and PHYC 120. PHYC 120 satisfies the TIER 1 natural science requirement in the University Core Curriculum. This program leads to a bachelor of science degree only. All students will be required to complete a survey designated by the department in the semester in which they graduate. 

MAJOR IN MATHEMATICAL SCIENCES, 54-58 hours

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MATH









165
166
215
217
259
267
320
374
411
471
498

Calculus 1
Calculus 2
Discrete Systems
Linear Algebra
Intro to Mathematical Software
Calculus 3
Probability
Differential Equations
Abstract Algebra 1
Real Analysis 1
Senior Seminar

4
4
4
4
3
4
4
3
3
4
2

Complete one option
Option 1: Mathematics, 15 hours

MATH

412
472

Abstract Algebra 2
Real Analysis 2

3
3

9 hours from

MATH





377
415
416 
441
445  
473
475

Complex Analysis (3)
Coding and Communication (3)
Theory of Numbers (3)
Geometry and Topology (3)
Differential Geometry (3)
Boundary Value Problems (3)
Topics Partial Dif Equations (3)


 

or as approved 

9




54 hrs
Mathematical science students are encouraged to take CS 120 and PHYC 120. PHYC 120 satisfies the TIER 1 natural science requirement in the University Core Curriculum. Students are strongly advised to deepen their understanding of aspects of the program by selecting additional courses in areas such as business, computer science, finance, economics, or physics. By selecting additional courses appropriately, a student can earn a related minor in computer science, physics, or foundations of business for actuarial science and mathematics majors.   
Option 2: Applied Mathematics, 18-19 hours

MATH

335
362

Mathematical Models
Numerical Analysis 1

3
3

Two courses from two blocks (four courses total)
Statistics

MATH


321
422
428
429

Mathematical Statistics (4)
Theory Sampling and Surveys (3)
Regression Time Series Models (3)
Analysis Variance Exp Design (3)


Discrete mathematics

MATH


412
415
416
456

Abstract Algebra 2 (3)
Coding and Communication (3)
Theory of Numbers (3)
Intro Operations Research (3)


Analysis

MATH



363
377
472  
473
475

Numerical Analysis 2 (3)
Complex Analysis (3)
Real Analysis 2 (3)
Boundary Value Problems (3)
Topics Partial Dif Equations (3)

12-13




57-58 hrs
Mathematical science students are encouraged to take CS 120 and PHYC 120. PHYC 120 satisfies the TIER 1 natural science requirement in the University Core Curriculum. Students are strongly advised to deepen their understanding of aspects of the program by selecting additional courses in areas such as business, computer science, finance, economics, or physics. By selecting additional courses appropriately, a student can earn a related minor in computer science, physics, or foundations of business for actuarial science and mathematics majors. 

MINOR IN FOUNDATIONS OF BUSINESS FOR ACTUARIAL SCIENCE
AND MATHEMATICS MAJORS, 22 hours

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ACC
ECON

FIN

MATH

201
201
202
300  
310
259
321

Principles of Accounting 1
Elementary Microeconomics
Elementary Macroeconomics
Principles of Finance
Investments 1
Intro to Mathematical Software
Mathematical Statistics

3
3
3
3
3
3
4




22 hrs
Students should complete MATH 320 to satisfy the prerequisite for MATH 321.

MINOR IN MATHEMATICS, 23-25 hours

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NO 

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MATH

165
166
267

Calculus 1
Calculus 2
Calculus 3

4
4
4

4 hours from

MATH

215
217

Discrete Systems (4)
Linear Algebra (4)

4

7-9 hours from

MATH























215
217
221
251
259
311
320
321
335
345
362
363
374
377
415
416
441  
445
456
460
471
472
473
475
497

Discrete Systems (4)
Linear Algebra (4)
Probability and Statistics (3)
Intro to Mathematics of Financ (2)
Intro to Mathematical Software (3)
Algebraic Structures (3)
Probability (4)
Mathematical Statistics (4)
Mathematical Models (3)
Survey of Geometries (4)
Numerical Analysis 1 (3)
Numerical Analysis 2 (3)
Differential Equations (3)
Complex Analysis (3)
Coding and Communication (3)
Theory of Numbers (3)
Geometry and Topology (3)
Differential Geometry (3)
Intro Operations Research (3)
History of Mathematics (3)
Real Analysis 1 (4)
Real Analysis 2 (3)
Boundary Value Problems (3)
Topics Partial Dif Equations (3)
Student Faculty Colloquium (1-6)


or approved MATH courses

7-9




23-25 hrs

TEACHER EDUCATION

Teaching programs require additional courses in educational methods. The professional education courses are included in this listing. See the Department of Educational Studies and Teachers College for the descriptions of these courses and other professional requirements of the teacher education program. 

TEACHING MAJOR IN MATHEMATICS, 47-48 hours

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MATH





165
166
215
217
221
250
496

Calculus 1
Calculus 2
Discrete Systems
Linear Algebra
Probability and Statistics
Advanced Pre-College Math
Capstone Math Teaching

4
4
4
4
3
3
3

Complete one option
Option 1: Middle school, 22 hours

MATH

   
   
  

201
202
310
316
360

Num Alg Prob Elem Teach
Data Geo Meas Elem Teach
Algebra Elem Mid Scl Teach
Num Thry Elem Mid Scl Teach 
Geometry Elem Mid Scl Teach

4
3
3
3
3

At least 6 hours from (as approved by advisor)

MATH





251
267
311
335
345
416
460

Intro to Mathematics of Financ (2)
Calculus 3 (4)
Algebraic Structures (3)
Mathematical Models (3)
Survey of Geometries (4)
Theory of Numbers (3)
History of Mathematics (3)

6





47 hrs
Option 2: Secondary school, 23 hours

MATH



267
311
335
345
460

Calculus 3
Algebraic Structures
Mathematical Models
Survey of Geometries
History of Mathematics

4
3
3
4
3

At least 6 hours from (as approved by advisor)

MATH














251
259
320
362
374
377
411
415
416
441 
445
456
471
473
475
497

Intro to Mathematics of Financ (2)
Intro to Mathematical Software (3)
Probability (4)
Numerical Analysis 1 (3)
Differential Equations (3)
Complex Analysis (3)
Abstract Algebra 1 (3)
Coding and Communication (3)
Theory of Numbers (3)
Geometry and Topology (3)
Differential Geometry (3)
Intro Operations Research (3)
Real Analysis 1 (4)
Boundary Value Problems (3)
Topics Partial Dif Equations (3)
Student Faculty Colloquium (1-6)







6





48 hrs
Students are encouraged to take CS 120 and PHYC 120. PHYC 120 satisfies the TIER 1 natural science requirement in the University Core Curriculum. All students will be required to take a comprehensive exam designated by the department. 

SENIOR HIGH, JUNIOR HIGH/MIDDLE SCHOOL EDUCATION PROGRAM

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Professional education sequence, 42 hours 

EDFO
EDJH
EDMU
EDPS

EDSE
MATH


420
385
205
251
390
380
150
331
393
395

Soc, Hist, Phil Found of Ed
Prin of Tchng in Mid Schl
Intro to Multicul Ed
Development Secondary
Educational Psychology
Princ of Tchng in Sec School
Intro Secondary Math Education
Technology Secondary Math
Teach Mathematics Middle Schl
Teach Mathematics Secondary

3
3
3
3
3
3
3
3
3
3

Student teaching

12




42 hrs
See Professional Education Assessment/Decision Points, for additional information.

LICENSE IN MIDDLE SCHOOL/JUNIOR HIGH MATHEMATICS, 24-31 hours

Students follow the elementary education Decision Points. 
Only open to candidates who currently hold or who are pursuing a license in elementary: intermediate education. Middle school/junior high licensure in mathematics will be granted when the following criteria are met: 

  • all requirements for the elementary intermediate license;
  • completion of the following mathematics content courses with a C- or better grade;
  • completion of the following mathematics content courses with a 2.5 minimum grade-point average;
  • completion of the professional education courses with a 2.5 minimum grade-point average;
  • passing score on the exam for middle school mathematics.

Decision Point 2 - Students must complete the following before registering for MATH 393:

  • Meet with a MJH Mathematics advisor to declare interest in the program and to review progress.
  • Complete all Decision Point 1 and 2 requirements for Elementary Education.
  • Complete the following mathematics content courses with a grade of C- or better and a grade-point average of 2.5 or better; MATH 161 or 165, 181, and 310.
  • A Calculus Presentation delivered to faculty members in the Department of Mathematical Sciences and receiving a score of "basic" or better.
  • In the digital portfolio, include a reflective artifact addressing what was learned in the above courses and the need for acquiring knowledge beyond the level taught in the middle grades.
  • In the digital portfolio, include a reflective artifact addressing what was learned about mathematics and teaching mathematics from the experience of preparing and delivering the Calculus Presentation.

Decision Point 4 - Students must complete the following to receive recommendation for licensure in middle school/junior high mathematics:

  • Meet with a MJH Mathematics advisor to review progress.
  • Complete all Decision Point 3 and 4 requirements for Elementary Education.
  • Complete student teaching in a middle school/junior high mathematics classroom or in a grade 5 or 6 elementary school classroom.
  • Complete all required mathematics content courses with a grade of C- or better and a grade-point average of  2.5 or better: MATH 161 or 165, 181, 310, 316, 330, and 360.
  • Complete professional education courses with a grade of C or better and a grade-point average of 2.5 or better; EDJH 385 and MATH 393.
  • In the digital portfolio, include one new artifact for each of seven of the ten INTASC principles, each with an accompanying rationale clearly labeled “DP3,” that addresses knowledge, performances, or dispositions related to teaching middle school mathematics.
  • Earn a passing score on the exam for Middle School Mathematics.

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Middle school/junior high content area, mathematics, 24-31 hours

MATH






 

161 
or
165
181
310
316
330
360 

Applied Calculus 1 (3)

Calculus 1 (4)
Elementary Probability Stats
Algebra Elem Mid Scl Teach
Num Thry Elem Mid Scl Teach
Technology Ele Mid School Math
Geometry Elem Mid Scl Teach

3-4
3
3
3
3
3





18-19 hrs
Professional education, 6-12 hours   

EDJH
MATH

385
393

Prin of Tchng in Mid Schl
Teach Mathematics Middle Schl

3
3

Additional student teaching

0-6





6-12 hrs




24-31 hrs
Additional student teaching may be waived if elementary student teaching is grade 5 or grade 6. 

MATHEMATICAL SCIENCES (MATH) 

108 Intermediate Algebra (3)
Reviews number sense, fundamental concepts of algebra, including rules for expressions and equations, linear and quadratic equations, relations and functions, integer exponents, radicals, and systems of equations. Offered credit/no credit only.         
    Prerequisite: two years of college preparatory mathematics in high school or equivalent.         
    Not open to students who have credit in MATH courses numbered higher than 108 except MATH 125.  

111 Pre-Calculus Algebra (3)
Reviews fundamental concepts of algebra; covers functions and their graphs, linear, power, quadratic, exponential, logarithmic, polynomial, and rational functions. Core Transfer Library: Mathematics (IMA 1601)         
    Prerequisite: MATH 108, appropriate score on the SAT/ACT, or appropriate scores on the mathematics placement test, or permission of the department chairperson.                
    Not open to students who have credit in MATH 132 or 161 or 165. 

112 Precalculus-Trigonometry (3) 
Trigonometric functions, identities, and equations; graphs of the trigonometric and inverse trigonometric functions; solutions of right and general triangles; polar coordinates; and complex numbers. Core Transfer Library: Mathematics (IMA 1608)
    Prerequisite: qualifying SAT/ACT score, or appropriate score on the mathematics placement test, or MATH 108 or 111, or permission of the department chairperson. 
    Not open to students who have credit in MATH 132 or higher except by permission of the department chairperson. 

125 Mathematics and Its Applications (3) 
A diverse course including statistics and other topics such as mathematical modeling, problem solving, finance, geometrical concepts, growth patterns, and applications to the physical sciences, social sciences, and economics. Core Transfer Library: Mathematics (IMA 1607)
    Recommended background: three years of college preparatory mathematics in high school.

132 Brief Calculus (3) 
Brief survey of differential and integral calculus. Emphasizes business applications of these topics. 
    Prerequisite: C- or better in MATH 111, or an appropriate score on the SAT/ACT or on the mathematics placement test, or permission of the department chairperson. 

150 Introduction to Secondary Mathematics Education (3)
An introduction to secondary mathematics teaching. Content includes constructing an informed vision of mathematics and mathematics teaching, developing basic skills for teaching mathematics, and beginning preparation for teacher licensure. 
    Prerequisite or parallel: MATH 165 or permission of the department chairperson. 

161 Applied Calculus 1 (3) 
Discussion of limits, derivatives, differentials, and definite and indefinite integrals. Focuses on the application of these topics in the applied sciences. Core Transfer Library: Mathematics (IMA 1604)
    Prerequisite: C- or better in MATH 111, or an appropriate score on the SAT/ACT or on the mathematics placement test, or permission of the department chairperson. 
    Not open to students who have credit in MATH 165. 

162 Applied Calculus 2 (3) 
Derivatives and integrals of transcendental functions with additional applications, techniques of integration, improper integrals, calculus in higher dimensions and series. Core Transfer Library: Mathematics (IMA 1605)
    Prerequisite: C- or better in MATH 112, or an appropriate score on the SAT/ACT or on the mathematics placement test, and C- or better in MATH 161 or 165, or permission of the department chairperson. 
    Not open to students who have credit in MATH 166. 

165 Calculus 1 (4) 
Differential calculus of algebraic and transcendental functions and applications, antidifferentiation and the Riemann integral. Includes the use of graphing calculators and computer software. Core Transfer Library: Mathematics (IMA 1602)
    Prerequisite: C- or better in MATH 111, 112 or sufficient background in algebra and trigonometry as evidenced by the student's SAT/ACT scores and/or score on the mathematics placement test, or permission of the department chairperson. 

166 Calculus 2 (4)
Standard techniques of integration, applications of the integral, numerical integration, sequences and series. Includes the use of graphing calculators and computer software. Core Transfer Library: Mathematics (IMA 1603)         
    Prerequisite: C- or better in MATH 165 or permission of the department chairperson.  

181 Elementary Probability and Statistics (3)
Algebra-based introduction to statistical applications through descriptive methods, probability, normal distributions, confidence intervals, hypotheses tests, regression, and correlation. Misuses of statistics and common probability misconceptions are discussed. Statistical experiments and simulations are conducted. Technology use is integrated throughout.         
    Prerequisite: MATH 108, or appropriate score on the SAT/ACT, or appropriate scores on the mathematics placement test, or permission of the department chairperson.  

201 Number, Algebra, and Probability for the Elementary Teacher (4)
In-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including concepts in number and operation, algebra, and probability. Use of selected concrete manipulatives and technology is included.         
    Prerequisite: appropriate score on the SAT/ACT, or appropriate score on the mathematics placement test, or credit in MATH 108, or permission of the department chairperson.                 
    Open only to option 1 mathematics teaching majors, or majors in elementary, special, or early childhood education. 

202 Data Analysis, Geometry, and Measurement for the Elementary Teacher (3) 
In-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including concepts in data analysis, geometry, and measurement. Use of selected concrete manipulatives and technology is included. 
    Prerequisite: MATH 201 with a C- or better grade.

207 Mathematics for the Teacher of the Exceptional Learner (4)
Development of concepts in number and operation, algebra, geometry, measurement, data analysis, and probability needed by teachers of exceptional learners. Use of selected concrete manipulatives and technology is included. 
    Prerequisite: qualifying ACT or SAT score, or appropriate score on the mathematics placement test, or MATH 108, or permission of the department chairperson. 
    Not open to students who have credit in MATH 201 or 202. 
    Open only to special education majors. 

215 Discrete Systems (4)
Topics from discrete mathematics, including formal logic, methods of proof, set theory, relations, recursion, combinatorics, and graph theory. A systematic development of number systems via equivalence classes is included as an application of these topics.         
    Prerequisite: C- or better in MATH 162 or 165, or permission of the department chairperson.  

217 Linear Algebra (4)
Theory and application of systems of linear equations, vector equations, linear transformations, vector spaces, and inner product spaces. Includes the use of computer software.         
    Prerequisite: C- or better in MATH 162 or 165, or permission of the department chairperson.  

221 Probability and Statistics (3)
Elementary probability theory, random variables, discrete and continuous probability distributions. Theory and applications of descriptive and inferential statistics. Statistical software and graphing calculator use is integrated throughout the course.         
    Prerequisite: C- or better in MATH 162 or 165, or permission of the department chairperson.  

250 Pre-College Mathematics from an Advanced Viewpoint (3)
In-depth treatment of concepts underlying common topics in the middle and high school mathematics curriculum. Topics include number systems, polynomial and transcendental functions, analytic geometry, theory of equations, and measurement.         
    Prerequisite: MATH 150 and 166 and 215.         
    Open only to mathematics teaching majors.  

251 Introduction to Mathematics of Finance (2)
Mathematical topics in finance as expected to be useful in financial decision-making in the future. Topics will include compound and simple interest, savings, mortgages, loans, equity, annuities, equations of value, yield rates, amortization, sinking funds, bonds, and current topics in finance as time permits. Emphasis will be on fundamental principles, calculations, and practical applications.         
    Prerequisite: C- or better in MATH 111 and 112, or appropriate score on the SAT/ACT, or appropriate scores on the mathematics placement test, or permission of the department chairperson.  

259 Introduction to Mathematical Software (3)
Basic introduction to mathematical software currently used for solving math-related problems on computers. Includes a regularly scheduled computer laboratory.         
    Prerequisite: C- or better in MATH 215 or permission of the department chairperson.  

267 Calculus 3 (4)
Multidimensional calculus and its applications. Topics include three-dimensional vector calculus, Gauss's theorem, Green's theorem, and Stoke's theorem. Includes the use of graphing calculators and computer software.                 
    Prerequisite: C- or better in MATH 166 or permission of the department chairperson. 

271 Mathematics Contest Problem Solving (1) 
Advanced mathematics problem-solving strategies for individuals and groups. Designed to prepare participants for the Putnam Exam and other collegiate mathematics contests. 
    Open to all students. 
    A total of 2 hours of credit may be earned, but no more than 1 in any one semester or term. 

298 Undergraduate Colloquium (1) 
A series of brief introductions to the mathematical landscape including glimpses of mathematics in the workplace. Topics are drawn from all areas of the mathematical sciences. 
    A total of 3 hours of credit may be earned, but no more than 1 in any one semester or term. 

299X Experimental/Developmental Topics (1-6) 
Topics relevant to the discipline. Course titles will be announced before each semester. 
    A total of 6 hours of credit may be earned. 

310 Topics in Algebra for the Elementary and Middle School Teacher (3) 
Development of algebraic concepts including variables, functions, and matrices, and applications of these topics in the elementary and middle school curriculum. 
    Prerequisite: MATH 202 with a C- or better grade. 

311 Algebraic Structures (3)
Consideration of the basic algebraic structures: groups, rings, integral domains, and fields. Examples of these structures and elementary proof will be emphasized as will polynomials over rings, integral domains, and the fields of real and complex numbers.                 
    Prerequisite: C- or better in MATH 215 and 217 or permission of the department chairperson. 

316 Topics in Number Theory for the Elementary and Middle School Teacher (3) 
The study of a collection of topics from the theory of numbers that have specific applications in the elementary and middle school curriculum. 
    Prerequisite: MATH 202 with a C- or better grade. 

320 Probability (4)
Probability theory for discrete and continuous sample spaces, random variables, density functions, distribution functions, marginal and conditional distributions, mathematical expectation, moment-generating functions, common distributions, sampling distribution theory, central limit theorem, t, chi-square, and F distributions.         
    Prerequisite: C- or better in MATH 166 or permission of the department chairperson.         
    Parallel: MATH 215.  

321 Mathematical Statistics (4)
Point and interval estimation, maximum likelihood, Neyman-Pearson Lemma, likelihood ratio tests, classical tests of significance, goodness-of-fit, contingency tables, correlation, regression, nonparametric methods, Bayesian methods.                 
    Prerequisite: C- or better in MATH 320 or permission of the department chairperson. 

330 Technology in Elementary and Middle School Mathematics (3) 
The use of technology in elementary and middle school mathematics, such as spreadsheets, calculators, algebraic or geometric modeling tools, educational software, and World Wide Web applications. 
    Prerequisite: MATH 202 with C- or better grade. 

331 Technology in the Teaching of Secondary Mathematics (3)
The use of technology in the teaching of secondary and middle school mathematics, such as spreadsheets, calculators, algebraic or geometric modeling tools, educational software, and World Wide Web applications.         
    Prerequisite: C- or better in MATH 250; admission to Teacher Education; permission to enroll in 300/400-level professional education courses.  

335 Mathematical Models (3)
Construction of mathematical models for use with problems in physics, chemistry, biology, and economics. Emphasizes the construction and interpretation of models. Existing computer software will be used. 
    Prerequisite: C- or better in MATH 166 and 217, or permission of the department chairperson.  

345 Survey of Geometries (4)
A comparative study of Euclidean and non-Euclidean geometries, their respective histories and technologies, and their applications in mathematics, the sciences, and modern life.         
    Prerequisite: C- or better in MATH 166 and 215 and 217 or permission of the department chairperson.  

351 Mathematics of Finance (4)
Mathematical theory of compound interest, force of interest, annuities, equations of value, yield rates, amortization, sinking funds, bonds, market derivatives, depreciation, and current topics in finance.         
    Prerequisite: C- or better in MATH 165 and 251 or permission of the department chairperson.                 
    Parallel: MATH 166. 

355 Topics in Actuarial Science (1-6) 
Selected topics in actuarial science with emphasis on individualized study for the actuarial exams given by the Society of Actuaries and the Casualty Actuarial Society. 
    Prerequisite: permission of the department chairperson. 
    A total of 4 hours of credit may be counted as electives for the major in actuarial science. 
    A total of 6 hours of credit may be earned. 

360 Topics in Geometry for the Elementary and Middle School Teacher (3) 
Investigation of selected topics in geometry and measurement, from both historical and contemporary perspectives, with applications in the elementary and middle school curriculum. 
    Prerequisite: MATH 202 with a C- or better grade. 

362 Numerical Analysis 1 (3)
Topics include error analysis, locating roots of equations, interpolation, numerical differentiation and integration, spline functions, smoothing of data. Includes programming of numerical algorithms.         
    Prerequisite: C- or better in MATH 162 or 166; and MATH 259 or CS 120; or permission of the department chairperson.  

363 Numerical Analysis 2 (3)
Topics include direct and iterative methods for solving systems of linear equations, eigenvalue problems; minimization of functions and linear programming. Includes programming of numerical algorithms.                 
    Prerequisite: C- or better in MATH 217 and 362 or permission of the department chairperson. 

368 Unpaid Professional Experience in Mathematical Sciences (1-8) 
Supervised unpaid work and learning experience as a practicing mathematician, statistician, or actuarial scientist. Practical problem-solving experience will be gained through an internship, practicum, or other such situation. Offered credit/no credit only. 
    Prerequisite: permission of the department chairperson.
    A total of 8 hours of credit may be earned in MATH 368 and 369 combined. 

369 Paid Professional Experience in Mathematical Sciences (1-8) 
Supervised paid work and learning experience as a practicing mathematician, statistician, or actuarial scientist. Practical problem-solving experience will be gained through an internship, practicum, or other such situation. Offered credit/no credit only. 
    Prerequisite: permission of the department chairperson. 
    A total of 8 hours of credit may be earned in MATH 368 and 369 combined. 

371 Intermediate Analysis (3)
Introduction to basic concepts of analysis: the real numbers, sequences, continuous functions, the derivative, and the Riemann integral.         
    Prerequisite: C- or better in MATH 166 and 215, or permission of the department chairperson.  

374 Differential Equations (3)
Introduction to nth-order ordinary differential equations, equations of order one, elementary applications, linear equations with constant coefficients, nonhomogeneous equations, undetermined coefficients, variation of parameters, linear systems of equations, and the Laplace transform. Use of standard computer software.         
    Prerequisite: C- or better in MATH 162 or 166 or permission of the department chairperson.  

377 Complex Analysis (3)
Algebra and geometric representation of complex numbers, properties of complex analytic functions, contour integration, power series and Laurent series, poles and residues, conformal mapping, and applications.                 
    Prerequisite: C- or better in MATH 267 or permission of the department chairperson. 

390 Honors Colloquium in Mathematics (1-6) 
Selected topics in mathematics with emphasis on individualized study. 
    A total of 6 hours of credit may be earned. 

391 Teaching and Learning Mathematics in the Elementary School (3) 
Development of pedagogical-content knowledge through national and state mathematics standards, curricular materials, instructional materials and methods, and assessment related to specific topics in elementary school mathematics. Class ideas applied in teaching situations. May be substituted for MATH 392. 
    Prerequisite: MATH 202 with a C- or better grade, admittance to Teacher Education; permission to enroll in 300/400-level professional education courses. 

392 Teaching Mathematics to Learners with Disabilities (3) 
Introduction to standards, instructional materials and methods, and assessment, emphasizing how these relate to the teaching of mathematics to learners with disabilities. Class ideas applied in teaching situations. Three one-hour lectures and one one-hour laboratory experience per week. May not be substituted for MATH 391. 
    Prerequisite: MATH 207 with a C- or better grade or both MATH 201 and 202 with a C- or better grade. Admittance to Teacher Education; permission to enroll in 300/400-level professional education courses. 
    Open only to special education majors. 

393 Teaching and Learning Mathematics in the Middle School (3) 
Introduction to national and state mathematics standards, curricular materials, instructional materials and methods, and assessment related to topics taught in middle school mathematics. 
    Prerequisite: for teaching major in mathematics option 1 or option 2, MATH 250 with a grade of C- or better; for middle school/junior high mathematics license, MATH 202 with a grade of C- or better; permission to enroll in 300/400-level professional education courses. 

395 Teaching and Learning Mathematics in the Secondary School (3)
Examination of national and state mathematics standards, curricular materials, and methods for teaching mathematics to secondary school students. Issues related to mathematics curriculum, instruction, and assessment of secondary school students. Class ideas applied in teaching situations.         
    Prerequisite: C- or better in MATH 250, and 311 or 310, and MATH 345 or 360, and 393; a minimum grade-point average of 2.5 in all mathematics courses to be applied to the major, and admittance to teacher education and permission to enroll in 300/400-level professional education courses.                 
    Parallel: EDJH 385 and EDSE 380. 

399 Theory and Practice in Middle School Mathematics (3) 
Combines theory and practice of teaching middle school mathematics. A deeper investigation into student learning and the development of mathematical concepts and procedures. Class ideas applied in teaching situations. 
    Prerequisite: MATH 202 or 250 with a grade of C- or better; MATH 391 or 393 with a grade of C- or better; a minimum grade-point average of 2.5 in all mathematics courses in the program; admission to Teacher Education; permission to enroll in 300/400-level professional education courses. 
    Parallel: EDJH 385. 

411 Abstract Algebra 1 (3) 
The theory of groups, including subgroups, cyclic groups, normal subgroups, cosets, Lagrange’s Theorem, quotient structures, homomorphisms, automorphisms, group actions, Sylow’s Theorems, structure of finite abelian groups, generators, and relations. 
    Prerequisite: MATH 215, 217; or permission of the department chairperson. 

412 Abstract Algebra 2 (3) 
An introduction to the theory of rings, including integral domains, division rings, and fields. Quotient fields of integral domains. Homomorphisms, ideals, and quotient structures. Factorization in commutative rings. Polynomial rings and field extensions. Aspects of Galois theory. 
    Prerequisite: MATH 411 or permission of the department chairperson. 

415 Mathematics of Coding and Communication (3) 
Exploration of applications of number theory, group theory, and linear algebra to areas such as cryptography and error-correcting codes; applications of graph theory to resource allocation and route planning; other possible topics selected by the instructor. 
    Prerequisite: MATH 215, 217; or permission of the department chairperson. 

416 Theory of Numbers (3) 
Topics include the division algorithm; positional notation; divisibility; primes; congruences; divisibility criteria; the sigma, divisor, and phi functions; diophantine equations; linear, polynomial, and simultaneous congruences; theorems of Fermat, Euler, Lagrange, and Wilson; quadratic reciprocity. 
    Prerequisite: MATH 215 or permission of the department chairperson. 

422 Theory of Sampling and Surveys (3) 
Survey designs; simple random, stratified, cluster, and systematic sampling; ratio estimates; regression estimates; cost and variance functions. 
    Prerequisite: MATH 321 or its equivalent. 

428 Regression and Time Series Models (3) 
Addresses regression topics that include simple and multiple linear regression, polynomial regression, regression diagnostics, and forecasting. Introduces time series topics that include exponential smoothing, auto-regressive, integrated, moving average (ARIMA) models, and forecasting. 
    Prerequisite: MATH 321 or equivalent. 

429 Analysis of Variance in Experimental Design Models (3) 
Multivariate normal distribution; quadratic forms; linear models; simple random, randomized block, Latin squares, factorial, split-plot, balanced incomplete block design; analysis of covariance; confounding; multiple comparison tests. 
    Prerequisite: MATH 321 or its equivalent. 

441 Geometry and Topology (3) 
Introduction to geometric topology, including piecewise linear structures, Euler’s formula, surfaces and solids, knots, graphs, and other topics. 
    Prerequisite: MATH 217, 267; or permission of the department chairperson. 

445 Differential Geometry (3) 
Fundamentals of differential geometry, as an extensive study of curves and surfaces in 3-space. Includes the use of computer visualization and emphasizes the importance of differential geometry in areas like relativity theory and modern physics. 
    Prerequisite: MATH 217, 267; or permission of the department chairperson. 

452 Mathematics of Life Contingencies 1 (4) 
Survival distributions, life tables; the mathematics of life insurance, life annuities, net premiums, and net premium reserves. 
    Prerequisite: MATH 321, 351, and a minimum grade-point average of 2.5 in all mathematics courses that are to be applied to the major. 

453 Mathematics of Life Contingencies 2 (4) 
Mathematics of multiple life functions, multiple decrement models, valuation theory for pension plans, insurance models including expenses, nonforfeiture benefits, and dividends. 
    Prerequisite: MATH 452. 

454 Mathematics of Investments (3) 
Mathematical analysis and actuarial principles of investments and asset management. 
    Prerequisite: MATH 320, 351; or permission of the department chairperson. 

456 Introduction to Operations Research (3)
Topics include linear programming models, the simplex method, duality theory, transportation and assignment problems, network optimization models. 
    Prerequisite: MATH 162 or 166, 217, or permission of the department chairperson. 

457 Actuarial Models 1 (4) 
Loss and frequency distributions, limited expected value, effects of inflation, parametric and non-parametric models, identification procedures for insurance company data, bootstrapping, Bayesian analysis, compound frequency, methods for censored and truncated data, classical and Bayesian credibility models, experience rating. 
    Prerequisite: MATH 321. 

458 Actuarial Models 2 (3) 
Basic functions related to actuarial models, common parametric models, maximum likelihood estimation for censored or truncated data, nonparametric estimation, hypothesis testing, models with co-variables, simulation, and other topics as time permits. 
    Prerequisite: MATH 321.

459 Models in Financial Economics (3) 
Mathematical and economic analysis of financial instruments and the management of financial and investment risk.
    Prerequisite: MATH 320, 351 or permission of the department chairperson.

460 History of Mathematics (3) 
The development of mathematics from prehistoric times to the seventeenth century. Topics may include number concepts and numeration, algebra, geometry, trigonometry, analytic geometry, and calculus. 
    Prerequisite: MATH 161 or 165. 

464 Numerical Methods for Differential Equations (3) 
Numerical methods for solving differential equations: finite difference and finite element discretization techniques; direct and iterative methods; analysis of convergence and stability; and computer implementation of numerical algorithms. 
    Prerequisite: MATH 374; MATH 259 or CS 120 or permission of the department chairperson. 

465 Topics in Computational Mathematics (1-6) 
Selected topics in computational mathematics, with an emphasis on applications of current mathematical software on computers to solve real-world problems. 
    Prerequisite: permission of the department chairperson. 
    A total of 6 hours of credit may be earned. 

471 Real Analysis 1 (4) 
Real and complex number systems: ordered sets, least upper bound property, fields, Archimedean property; Basic topology: cardinality, metric spaces, completeness, compactness, connectedness; Numerical sequences and series: convergence tests, upper-lower limits; Continuity: continuous functions, uniform continuity, Intermediate and Extreme Value Theorems; Differentiation: derivative, Mean Value Theorem, 1'Hospital's Rule, Taylor's Theorem. 
    Prerequisite: MATH 215, 267; or permission of the department chairperson. 

472 Real Analysis 2 (3) 
The Riemann-Stieltjes integral and Fundamental Theorem of Calculus. Sequences and series of functions. Differential calculus of functions of several variables. Inverse and implicit function theorems. Extremum problems. Lebesgue integration and comparison with the Riemann integral. 
    Prerequisite: MATH 471. 

473 Boundary Value Problems (3) 
Fourier Series and integrals, heat and wave equations in one dimension, Laplace’s equation in two dimensions, problems in higher dimensions, numerical methods of solving boundary value problems. 
    Prerequisite: MATH 374. 

475 Topics in Partial Differential Equations (3) 
Classical solution techniques for linear PDEs. Topics include first- and second-order equations, method of characteristics, special functions, orthogonal polynomials, transforms, Green’s functions, and fundamental solutions. A computer algebra system is utilized. 
    Prerequisite: MATH 267, 374; or permission of the department chairperson.

496 Capstone Course for Mathematics Teaching Majors (3)
Accompanies the student teaching experience of mathematics teaching majors. 
    Prerequisite: MATH 395. 
    Parallel: EDSE 460, 465.

497 Student-Faculty Colloquium (1-6) 
Participatory colloquium experience for motivated students. A contemporary topic of broad mathematical interest is chosen each semester. Each student is paired with a faculty member. These pairs work together to develop and present components of the semester-long course. 
    Prerequisite: MATH 267 or permission of the department chairperson. 
    A total of 6 hours of credit may be earned. 

498 Senior Seminar (2) 
Development of a broad, connected, contemporary perspective of mathematics and its applications. Includes a variety of readings, special lectures, and discussions. Each student will participate in a substantial project, presented both in oral and written forms. 
    Prerequisite: senior standing or permission of the department chairperson. 
    Open only to mathematical sciences majors. 

499 Reading and Honors (1-8) 
Juniors and seniors, with the approval of the mathematical sciences department, may enroll for special advanced work not offered in courses at the 300- and 400-levels. 
    Prerequisite: approval of the department chairperson. 
    A total of 8 hours of credit may be earned. 
    Open only to juniors and seniors.