Undergraduate Course Catalog

Mathematical Sciences

S. Stump, 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, mathematics teaching, and mathematical sciences. The department’s minors in mathematics is open to non-departmental majors. In conjunction with the Department of Economics, the department offers a major in mathematical economics, see interdepartmental programs.

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 a variety of choices, with 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.

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 MATHS 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 minor or major program.

All majors will be required to take a comprehensive exam designated by the department.


MAJOR IN ACTUARIAL SCIENCE, 59-60 hours

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CR HRS

MATHS












RMI

165
166
215
217
251
259
267
320
321
351
452
457   
498
270
371

Calculus 1
Calculus 2
Discrete Sys
Lin Algebra
Intr Mth Fin
Mth Software
Calculus 3
Probability
Math Stat
Math Finance
Life Cont 1
Act Model 1
Senior Sem
Prin R M I
Life/Health

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

6-7 hours from

CS  
MATHS   
   
  
  




ECON

120
355
362
374
428
453
454
458
465
424 

Comp Sci 1 (4)
Top Act Sci (1-6)
Numer Anls 1 (3)
Dif Equation (3)
Reg Time Ser (3)
Life Cont 2 (4)
Math Invest (4)
Act Model 2 (3)
Top Cmp Math (1-6)
Econometrics (3)

or as approved

6-7


59-60 hrs
Students may earn up to 6 credits for MATHS 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, MATHS 428 or ECON 424, FIN 300 and one from MATHS 454 or FIN 310. Other electives from the graduate actuarial science courses, business and economics are encouraged. Students are encouraged to take CS 120 and PHYCS 120. PHYCS 120 satisfies the natural science requirement in the University Core Curriculum. This program leads to a bachelor of science degree only.


MAJOR IN MATHEMATICAL SCIENCES, 53-57 hours

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MATHS










165
166
215
217
259
267
320
374
411
471
498

Calculus 1
Calculus 2
Discrete Sys
Lin Algebra
Mth Software
Calculus 3
Probability
Dif Equation
Abstr Alg 1
Real Anls 1
Senior Sem

4
4
4
4
3
4
4
3
3
3
2

Complete one option
Option 1: Mathematics, 15 hours

MATHS

412
472

Abstr Alg 2
Real Anls 2

3
3

9 hours from
MATHS






377
415
416 
441
445  
473
475
Complex Anl (3)
Mth Code Com (3)
Thry Numbers (3)
Geom Topol (3)
Diff Geom (3)
Bdry Val Pbm (3)
P D E (3)

or as approved

9


53 hrs
Mathematical Science students are encouraged to take CS 120 and PHYCS 120. PHYCS 120 satisfies the 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 in Business for Actuarial Science and Mathematics Majors.

Option 2: Applied Mathematics, 18-19 hours

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MATHS

 

335
362

Math Models
Numer Anls 1

3
3

Two courses from two blocks
(four courses total)
Statistics
MATHS



321
422
428
429
Math Stat (4)
Sampling (3)
Reg Tim Ser (3)
Exp Designs (3)
Discrete mathematics
MATHS



412
415
416
456
Abstr Alg 2 (3)
Mth Code Com (3)
Thry Numbers (3)
Intro Op Res (3)
Analysis
MATHS




363
377
472  
473
475
Numer Anls 2 (3)
Complex Anl (3)
Real Anls 2 (3)
Bdry Val Pbm (3)
P D E (3)





12-13


56-57 hrs
Mathematical Science students are encouraged to take CS 120 and PHYCS 120. PHYCS 120 satisfies the 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 in 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

MATHS

FIN

201
201
202
259
321
300  
310

Prin Acct 1
Elem Micro
Elem Macro
Mth Software
Math Stat
Prin Fin 1
Invest 1

3
3
3
3
4
3
3


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


MINOR IN MATHEMATICS, 23-25 hours

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NO 

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MATHS


165
166
267

Calculus 1
Calculus 2
Calculus 3

4
4
4

4 hours from

MATHS

215
217

Discrete Sys (4)
Lin Algebra (4)


4

7-9 hours from

MATHS
























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 Sys (4)
Lin Algebra (4)
Pbty Stats (3)
Intr Mth Fin (2)
Mth Software (3)
Alg Struct (3)
Probability (4)
Math Stat (4)
Math Models (3)
Survey Geom (4)
Numer Anls 1 (3)
Numer Anls 2 (3)
Dif Equation (3)
Complex Anl (3)
Mth Code Com (3)
Thry Numbers (3)
Geom Topol (3)
Diff Geom (3)
Intro Op Res (3)
Hist of Math (3)
Real Anls 1 (3)
Real Anls 2 (3)
Bdry Val Pbm (3)
P D E (3)
Stu-Fac Col (1-6)

or approved MATHS 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, 46-47 hours

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MATHS






165
166
215
217
221
250
498

Calculus 1
Calculus 2
Discrete Sys
Lin Algebra
Pbty Stats
Precoll Math
Senior Sem

4
4
4
4
3
3
2

Complete one option
Option 1: Middle school, 22 hours

MATHS
   
   
  

201
202
310
316
360

Num Alg Prob
Dat Geo Meas
Top Alg EMST
Num Thy EMST 
Top Geo EMST

4
3
3
3
3

At least 6 hours from (as approved by advisor)

MATHS






251
267
311
335
345
416
460

Intr Mth Fin (2)
Calculus 3 (4)
Alg Struct (3)
Math Models (3)
Survey Geom (4)
Thry Numbers (3)
Hist of Math (3)







6


46 hrs

Students are encouraged to take CS 120 and PHYCS 120. PHYCS 120 satisfies the natural science requirement in the University Core Curriculum.

Option 2: Secondary school, 23 hours

MATHS




267
311
335
345
460

Calculus 3
Alg Struct
Math Models
Survey Geom
Hist of Math

4
3
3
4
3

At least 6 hours from (as approved by advisor)

MATHS















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

Intr Mth Fin (2)
Mth Software (3)
Probability (4)
Numer Anls 1 (3)
Dif Equation (3)
Complex Anl (3)
Abstr Alg 1 (3)
Mth Code Com (3)
Thry Numbers (3)
Geom Topol (3)
Diff Geom (3)
Intro Op Res (3)
Real Anls 1 (3)
Bdry Val Pbm (3)
P D E (3)
Stu-Fac Col (1-6)
















6


47 hrs

Students are encouraged to take CS 120 and PHYCS 120. PHYCS 120 satisfies the natural science requirement in the University Core Curriculum.


EDUCATION PROGRAM FOR TEACHING MAJOR IN
MATHEMATICS

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Professional education sequence, 42 hours

MATHS
EDMUL
EDPSY

EDJHM
MATHS

EDFON
MATHS
EDSEC

150
205
251
390
385
331
393
420
395
380

Int Sec Math
Multi Educ
Dev Sec Ed
Educ Psychol
Prin Mid Sch
Tech Sec Mat
Tch Math MS
Fnds of Educ
Tch Math Sec 
Prin Sec Sch

3
3
3
3
3
3
3
3
3
3

Student teaching

12


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


MIDDLE SCHOOL/JUNIOR HIGH MATHEMATICS
LICENSE, 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 PRAXIS II exam for middle school mathematics.

Decision Point 2 - Students must complete the following before registering for MATHS 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; MATHS 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: MATHS 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; MATHS 393 and EDJHM 385. 
  • 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 PRAXIS II exam for Middle School Mathematics.

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NO 

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CR HRS

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

MATHS







165 
or
161
181
310
316
330
360 

Calculus 1 (4)

Appl Calc 1 (3)
El Prob Stat
Top Alg EMST
Num Thy EMST
Tech E M S
Top Geo EMST



3-4
3
3
3
3
3


18-19 hrs

Professional education, 6-12 hours

MATHS
EDJHM

393
385

Tch Math MS
Prin Mid Sch

3
3

Additional student teaching

0-6


6-12 hrs

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


MATHEMATICAL SCIENCES (MATHS)

108 Intermediate Algebra. (3)
Reviews factoring, quadratic equations and inequalities, relations and functions, rational exponents, systems of linear equations, and exponential and logarithmic functions. Offered credit/no credit only. 
    Recommended background: two years of college preparatory mathematics in high school or the equivalent. 
    Not open to students who have credit in MATHS courses numbered higher than 108 except MATHS 125.

111 Pre-Calculus Algebra. (3)
Such topics as polynomial functions and equations, exponential and logarithmic functions, determinants, systems of equations and inequalities, mathematical induction, the binomial theorem, permutations and combinations, and progressions. 
    Prerequisite: MATHS 108, or appropriate score on the SAT/ACT or mathematics placement test, or permission of the department chairperson. 
    Not open to students who have credit in MATHS 161 or higher.

112 Precalculus-Trigonometry. (3)
Trigonometric functions, identities, and equations; graphs of the trigonometric and inverse trigonometric functions; solution of right and general triangles; polar coordinates; and complex numbers. 
    Prerequisite: MATHS 111, or appropriate score on the SAT/ACT or mathematics placement test, or permission of the department chairperson. 
    Not open to students who have credit in MATHS 161 or higher.

125 Mathematics and Its Applications. (3)
University Core Curriculum course including such topics as mathematical modeling, problem solving, geometrical concepts, growth patterns, and applications to the physical sciences, social sciences, and economics. 
    Recommended background: three years of college preparatory mathematics in high school.

132 Brief Calculus. (3)
Brief survey of differential and integral calculus. Emphasizes applications. 
    Prerequisite: MATHS 111.

136 Mathematics for Business. (4)
Topics in mathematics particularly suited to the needs of business majors, including mathematics of finance, probability, and calculus. 
    Prerequisite: MATHS 111, an appropriate mathematics score on the ACT or SAT, or an appropriate college algebra score on the mathematics placement test.

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: MATHS 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. 
    Prerequisite: MATHS 112, or appropriate score on the SAT/ACT on mathematics placement test, or permission of the department chairperson. 
    Not open to students who have credit in MATHS 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. 
    Prerequisite: MATHS 161 or 165. 
    Not open to students who have credit in MATHS 166.

165 Calculus 1. (4)
Differential calculus of algebraic and transcendental functions and applications, antidifferentiation and the Riemann integral. The course includes the use of graphing calculators and computer software
    Prerequisite: MATHS 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.

166 Calculus 2. (4)
Standard techniques of integration, applications of the integral, sequences and series, indeterminate forms, and numerical methods. Includes the use of graphing calculators and computer software. 
    Prerequisite: MATHS 165.

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: qualifying ACT or SAT score, or appropriate score on the mathematics placement test, or MATHS 108, 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: qualifying ACT or SAT score, or appropriate score on the mathematics placement test, or MATHS 108, or permission of the department chairperson. 
    Open only to 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: MATHS 201 with a C- or better grade. 
    Not open to students who have credit in MATHS 203.

203 Data Analysis, Geometry, and Measurement for the Primary Teacher. (2)
In-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including selected concepts in data analysis, geometry, and measurement. Use of selected concrete manipulatives and technology is included. 
    Prerequisite: MATHS 201 with a C- or better grade. 
    Not open to students who have credit in MATHS 202.

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 MATHS 108, or permission of the department chairperson. 
    Not open to students who have credit in MATHS 201, 202, or 203. 
    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: MATHS 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: MATHS 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: MATHS 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: MATHS 150, 166, 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: MATHS 111, 112, or equivalent, or permission of the department chairperson.

259 (159) 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: MATHS 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: MATHS 166.

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: MATHS 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: MATHS 215, 217.

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: MATHS 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: MATHS 166, 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: MATHS 320.

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: MATHS 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: MATHS 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 or parallel: MATHS 166, 217.

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: MATHS 166, 215, 217.

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: MATHS 165, 251 or permission of the department chairperson. 
    Prerequisite or parallel: MATHS 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. 
    A total of 4 hours of credit may be counted as electives for the major in actuarial science. 
    Prerequisite: permission of the department chairperson. 
    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: MATHS 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: MATHS 162 or 166; and MATHS 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: MATHS 217, 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 MATHS 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 MATHS 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: MATHS 166, 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: MATHS 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: MATHS 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 MATHS 392. 
    Prerequisite: MATHS 202 or 203 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 MATHS 391. 
    Prerequisite: MATHS 207 with a C- or better grade or both MATHS 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, MATHS 250 with a grade of C- or better; for middle school/junior high mathematics license, MATHS 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: MATHS 311 or 310, 345 or 360, 393, a minimum grade-point average of 2.5 in all mathematics courses are to be applied to the major, and admittance to teacher education and permission to enroll in 300/400-level professional education courses.

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: MATHS 250 or 202 with a grade of C- or better; MATHS 393 or 391 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: EDJHM 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: MATHS 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: MATHS 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: MATHS 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: MATHS 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: MATHS 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: MATHS 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: MATHS 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: MATHS 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: MATHS 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: MATHS 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: MATHS 452.

454 Mathematics of Investments. (4)
Mathematical analysis and actuarial principles of investments and asset management. 
    Prerequisite: MATHS 320, 351; or permission of the department chairperson.

456 Introduction to Operations Research. (3)
Optimization techniques of linear programming, dynamic programming, and integer programming. Optimal solutions of PERT-CPM networks. Optimal decision strategies. 
    Prerequisite: MATHS 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: MATHS 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: MATHS 321.

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: MATHS 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; computer implementation of numerical algorithms. 
    Prerequisite: MATHS 374; MATHS 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. (3)
Properties of the real numbers. Cardinality. Topological properties of metric spaces: compactness, completeness, connectedness. Sequences and series. Continuous functions. Differential calculus of real- and vector-valued functions of one real variable. 
    Prerequisite: MATHS 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: MATHS 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: MATHS 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: MATHS 374, 267; or permission of the department chairperson.

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: MATHS 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.