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Mathematics Degree
Bachelor of Science (B.S.)
Under Construction
General Statement: The objectives of the Mathematics Program are (1) to provide training to enable graduates to be employed by any of a number of private industries, government agencies, foundations, and institutions requiring high-level quantitative skills and a highly developed ability to think critically and logically; (2) to provide training to enable graduates to enter graduate school in mathematics or related areas; (3) to provide training to enable graduates to assume careers as teachers of mathematics in secondary schools; (4) to develop proficiency in basic mathematical operations and develop skills in the use of formulas for the solution of problems; (5) to provide science and engineering majors the mathematical skills required by their various programs of study.
Departmental Requirements 38 Semester Hours
For Bachelor of Science
Mathematics
The curriculum for a B.S. degree in Mathematics consists of a minimum of 120 semester hours, of which 42 must be at the 3000 or 4000 level. A minimum of 38 semester hours must be in Mathematics or Statistics, exclusive of MATH 1005, 1115, 1710, 1720, and 1730 with at least 27 of these being at the 3000 or 4000 level, exclusive of MATH 3710, 4724, and 4750. Note that Computer Science 3900 may be used to satisfy upper level course requirements for the major in Mathematics. The 38 hours in Mathematics are differentiated into a required core and an appropriate specialization. Further requirements include 12 hours (6 hours for teacher certification candidates) of Computer Science and 8 hours of Physics. Also it is strongly recommended that the student include related areas (RA’s) of interest in the program of study. Because of the very tight prerequisite structure, no major program in Mathematics should be started without first consulting a major advisor. No Mathematics or Statistics course in which a grade below C is earned will be counted towards meeting the Mathematics major core requirements.
The Mathematics core consists of a calculus sequence, an introduction to real analysis, courses in linear and abstract algebra, a sequence in either advanced calculus or modern algebra, and a senior project. A methods course in the teaching of mathematics is required for those who are certifying to teach. In addition to successfully completing 38 hours of course work (grade C or above), the major must pass a written comprehensive examination on the core requirements.
Students who minor in Mathematics must earn at least 23 or 26 semester hours: 11 or 14 semester hours of calculus depending on the sequence taken and a minimum of 12 semester hours of 3000 or 4000 level MATH or STAT courses, exclusive of MATH 3710, 4724, and 4750. Computer Science 3900 may be used to satisfy upper level course requirements for the minor in Mathematics.
Besides the general program where the recommended RA’s (related areas) are pre-medicine, pre-law, etc., there are four options of specialization.
a) The pure Mathematics option includes MATH 4310 and 4530, as well as both the sequences MATH 4410-4420 and 4640-4650 in the required core. The recommended RA’s include computer science, physics, and philosophy.
b) The applied Mathematics option includes MATH 3120, 4560, and 4570, as well as MATH 4410-4420 in the required core. The recommended RA’s include engineering, physics, computer science, and chemistry.
c) The statistics option allows the student to use STAT 4210-4220 to satisfy the sequence requirement. The recommended RA’s include pre-actuarial science, general business, sociology, and psychology.
d) The secondary mathematics teacher option includes COMP 3200, STAT 3110, and MATH 3810, 4410, 4420, and 4750 in the required core. Students seeking teacher certification must apply in writing to the College of Education, usually in the sophomore year. At the time of applying they must have a 2.75 cumulative grade point average and must have passed the Pre-Professional Skills Test (PPST) or the Computer-Based Academic Skills Assessments Test (CBT). Students who have previously earned a 21 on the ACT, 22 on the Enhanced ACT, or a combined 990 on the verbal and mathematics portions of the SAT are exempt from the PPST and the CBT. Formal admission to the Teacher Education Program is a prerequisite for enrolling in upper-division certification courses.
Students must pass PRAXIS II exam before they can enroll in student teaching. Students must complete nine semester hours of enhanced student teaching with an eight-week placement at the secondary level and a seven-week placement at the middle school level. Successful completion of the program results in licensure to teach grades 7-12. For a complete list of requirements for admission to and retention in the Teacher Education Program, see the College of Education section.
General Education Core
Communications (9 hours)
ENGL 1010, 1020 Freshman English I, II 6
(minimum grade of C in each)
COMM 2200 Public Speaking 3
Humanities and/or Fine Arts (9 hours)
ENGL 2110-2322 Sophomore Literature 3
Elective From approved list. 3
Elective From approved list. 3
Social and Behavioral Science (6 hours)
ECON 2010 Principles of Economics I 3
Elective From approved list. 3
History (6 hours)
HIST 2010 American History I 3
HIST 2020 American History II 3
Natural Science (8 hours)
PHYS 2110/2111 General Physics I 4
PHYS 2120/2111 General Physics II 4
Mathematics (3 hours)
MATH 1910 Calculus I, Alternative 4
(Minimum grade of C.)
Orientation (1 hour)
ASOR 1001 Orientation for Science Majors 1
(Teacher certification students should take EDCI 1010.)
--------------------------------------------------------------------------------
Total General Education Hours 42
Upper–division Admission
For admission into the upper-division program of the Mathematics major, students must complete all of the requirements listed above under General Education Core. In addition, they must have removed all high school deficiencies, passed all required remedial/developmental courses, earned a cumulative grade point average of at least 2.0 on college-level course work, and completed the Rising Junior Examination. They must also have earned a grade of C or better in MATH 1910, 1920 and 2110.
Major Core (27, 24 for teacher certification candidates)
MATH 3510 Intermediate Analysis 3
MATH 3610 Linear Algebra I 3
MATH 3620 Linear Algebra II 3
(Not required for teacher certification candidates)
MATH 3640 Abstract Algebra 3
MATH 4410, 4420, or Advanced Calculus I, II, or 6
MATH 4640, 4650, or Modern Algebra I, II or
STAT 4210, 4220 Statistical Methods I, II
(MATH 4410, 4420 required of teacher
certification candidates)
MATH 4500 Senior Project 3
ELECTIVES 6
(teacher certification candidates take STAT 3110 and MATH 3810)
Suggested courses in areas of specialization may be obtained by consulting the major advisor.
Professional Education Core (37)
Requirements for Teacher certification students, only.
PSYC 2420 Human Growth& Learning 3
EDCI 2010 History & Foundation of Education 3
EDCI 3870 Curriculum Development 3
EDSE 3330 Education of Exceptional Children 3
PSYC 3120 Measurement/Evaluation in Schools 3
EDAD 4000 Professional Rights and Responsibilities 3
EDRD 4910 Reading & Study in Secondary School 3
EDCI 4190 Technology in the Schools 2
MATH 4724 Student Teaching of Mathematics 9
EDCI 4705 Educational Seminar 3
MATH 3710 Teaching Mathematics in the Secondary Schools 3
Bachelor of Science Degree in Mathematics
Suggested Four-Year Plan
FRESHMAN YEAR
Fall Semester HR Spring Semester HR
*MATH 1910 4 MATH 1920 4
ENGL 1010 3 ENGL 1020 3
HIST 2010 3 HIST 2020 3
COMP 2100 3 COMP 2110 3
ASOR 1001 1 HUMANITIES ELECTIVE 3
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14
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16
*MATH 1710 and/or 1720 must be taken prior to MATH 1910 if need is indicated.
SOPHOMORE YEAR
Fall Semester HR Spring Semester HR
MATH 2110 3 COMM 2200 3
ENGL 2010 3 HUMANITIES ELECTIVE 3
PHYS 2110, 2111 4 PHYS 2120, 2121 4
COMP 2120 3 ECON 2010 3
SOC SCI EL 3 ELECTIVE, ANY LEVEL 3
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--------------------------------------------------------------------------------
16
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16
JUNIOR YEAR
Fall Semester HR Spring Semester HR
MATH 3610 3 MATH 3620 4
COMP 3200 3 MATH 3510 3
ELECTIVES, ANY LEVEL 3 MATH 3640 3
HUMANITIES ELECTIVE 3
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--------------------------------------------------------------------------------
15
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15
SENIOR YEAR
FALL SEMSTER HR SPRING SEMESTER HR
MATH 4410 or 4640 or MATH 4420 or 4650 or
STAT 4210 3 STAT 4220 3
MATH 4500 3 MATH ELECTIVE 3000/4000 3
MATH ELECTIVE, 3000/4000 3 ELECTIVES, 3000/4000 8
ELECTIVES, 3000/4000 5
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14
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14
Bachelor of Science Degree in Mathematics
With Teacher Certification
Licensure for Grades 7-12
Suggested Four-Year Plan (122)
FRESHMAN YEAR
Fall Semester HR Spring Semester HR
*MATH 1910 4 MATH 1920 4
ENGL 1010 3 MATH 1005 1
HIST 2010 3 ENGL 1020 3
HUMANITIES ELECTIVE 3 HIST 2020 3
EDCI 1001 1 COMP 2100 3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
14
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
14
*MATH 1710 and/or 1720 must be taken prior to MATH 1910 if need is indicated.
SOPHOMORE YEAR
Fall Semester HR Spring Semester HR
MATH 2110 3 COMM 2200 3
ENGL 2010 3 HUMANITIES ELECTIVE 3
PHYS 2110, 2111 4 PHYS 2120, 2121 4
PSYC 2420 3 ECON 2010 3
SOC SCI EL 3 EDCI 2010 3
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--------------------------------------------------------------------------------
16
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
16
JUNIOR YEAR
Fall Semester HR Spring Semester HR
MATH 3510 3 MATH 3640 3
MATH 3610 3 MATH 4410 3
PSYC 3120 3 MATH 3810 3
STAT 3110 3 MATH 4750 3
EDAD 4910 3 EDSE 3330 3
EDCI 3870 3 EDCI 4190 2
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
18
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
17
SENIOR YEAR
FALL SEMSTER HR SPRING SEMESTER HR
COMP 3200 3 MATH 4724 9
MATH 4420 3 EDCI 4705 3
MATH 4500 3
MATH 3710 3
EDAD 4000 3
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15
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12
Course Descriptions
Mathematics (MATH)
MATH 1001 The Mathematics of Drugs and Solutions (1) (Formerly MATH 110). A course in measurements, calculations, and related topics for those entering the nursing profession. Calculations include the metric apothecary and home-type units, as well as determining IV rates, solution strengths, and miscellaneous procedures. Prerequisites: two years of high school algebra or one year of algebra and one year of geometry, or the equivalent. Course cannot be applied to satisfying the University mathematics requirement. Offered in fall and spring.
MATH 1005 Mathematics Education Orientation (1) (Formerly MATH 192). An introduction to the Mathematics teacher education program, including field experience. Prerequisite: interest in becoming a mathematics teacher. Offered in spring.
MATH 1013 Contemporary Mathematics (3). An Introduction to the mathematics used in our society. It includes elements of mathematical thought, inductive and deductive reasoning, and problem solving. Some of the topics included are graphics, counting techniques, number sequences, probability and statistics. This course satisfies the general education mathematics requirement. Prerequisites: Two years high school algebra or the equivalent, or one year of high school algebra and one year geometry or the equivalent. Offered in the fall, spring, and summer.
MATH 1110 College Algebra I (3). Graphs, relations, functions, inequalities, polynomials, exponents, radicals, logarithms, and exponential functions. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one year of geometry, or the equivalent. Offered in fall, spring, and summer.
MATH 1111 Honors College Algebra I (3). The Honors version of MATH 1110. Enrollment is limited to members of the University Honors College. Offered in fall.
MATH 1115 Fundamentals of Problem-Solving (1) (Formerly MATH 191). An introduction to Polya theories with emphasis on solving problems using mathematical methods. Prerequisite: 3 semester hours of college-level mathematics or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1120 College Algebra II (3). Rational functions, conic sections, systems of equations and inequalities, matrices and determinants, and an introduction to discrete mathematics. Prerequisite: grade of C or better in MATH 1110 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1121 Honors College Algebra II (3). The Honors version of MATH 1120. Enrollment is limited to members of the University Honors College. Offered on demand.
MATH 1140 Analytic Geometry and Trigonometry (3) (Formerly MATH 114). A survey of analytic geometry and trigonometry, including conic sections, connections among right triangle ratios, variation, periodic and circular functions, and the use of appropriate calculators and computers. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one of geometry, or the equivalent. Offered in fall and spring.
MATH 1410, 1420 Structure of the Number System I, II (3, 3). Set theory; relations; functions; inverses; order properties; systems of numeration; rational and irrational numbers; elementary number theory; mathematical systems; algorithms for the fundamental operations on whole numbers, integers, fractions, decimals, percent, ratio and proportion; equations; problem-solving; measurement in the metric system; elements of algebra; plane and solid geometry; elementary statistics. Prerequisite: For MATH 1410: Two years of high school algebra or the equivalent or one year high school algebra and one year geometry or the equivalent. For MATH 1420: MATH 1410. MATH 1410 Offered in fall, spring, and summer. MATH 1420 Offered in fall and spring.
MATH 1610 Introduction to Discrete Mathematics (3). A study of sets, relations and functions, mathematical induction, Boolean algebra and Boolean functions. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one of geometry, or the equivalent. Offered on demand.
MATH 1710 Precalculus Mathematics I (3). A course which with MATH 1720 provides the student with the foundation necessary to enter the calculus sequence. The topics include the study of polynomial, rational, exponential and logarithmic functions, and matrices. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one year of geometry, or the equivalent. Offered in fall, spring, and summer.
MATH 1720 Precalculus Mathematics II (3). A continuation of MATH 1710. Topics include right triangle trigonometry, trigonometric functions, analytic geometry, conic sections, sequences, and notation. Prerequisite: grade of C or better in MATH 1710 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1730 Precalculus Mathematics, Alternate (3). Integrated college algebra and trigonometry. This course provides the student with the background necessary to enter the calculus sequence. Topics include polynomials; rational functions; exponential, logarithmic, and trigonometric functions; analytic geometry; and conic sections. Prerequisites: high school algebra II, geometry, and trigonometry, or the equivalent. Offered in fall and spring.
MATH 1830 Basic Calculus I (3). An introduction to the basic concepts of differential and integral calculus, with applications oriented towards economics, business, and the social sciences. Prerequisite: grade of C or better in MATH 1110 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1910 Calculus I, Alternate (4) (Formerly MATH 1910). Part of the sequence MATH 1910, 1920 recommended for Mathematics, Physics, Chemistry, and Biology majors. Topics include functions, graphs, limits, derivatives with applications, and the definite integral with applications. Prerequisite: grade of C or better in MATH 1720 or 1730 or permission of the Department Head. Offered in fall.
MATH 1915 Calculus and Analytical Geometry (4). Part of the sequence MATH 1915, 1925, 2115, 2125, which emphasizes application to the physical sciences. Topics include functions, graphs, limits, derivatives, the definite integral, and rational functions including applications. Prerequisite: grade of C or better in MATH 1720 or 1730 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1920 Calculus II, Alternate (4). Study of derivatives and integrals of the trigonometric, logarithmic, and exponential functions, techniques of integration, sequences, and series. Course is part of the series MATH 1910, 1920, 2110, recommended for all Mathematics, Physics, Chemistry, and Biology majors. Prerequisite: grade of C or better in MATH 1910 or permission of the Department Head. Offered in spring.
MATH 1925 Calculus II (4). Further applications of definite integral, derivatives and integrals of transcendental functions, techniques of integration, and polar coordinates. Prerequisite: grade of C or better in MATH 1910 or 1915 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 2110 Calculus III, Alternate (3). Vector functions, three- dimensional space, partial derivatives, multiple integrals, line integrals, and applications. Part of the sequence MATH 1910, 1920, and 2110 recommended for all Mathematics, Physics, Biology, and Chemistry majors. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered in fall.
MATH 2115 Calculus III (3). Infinite sequences and series, vectors in two- and three-dimensional space, the calculus of a vector function, and applications. Prerequisite: grade of C or better in MATH 1925 or permission of the Department Head. Offered in fall, spring, summer.
MATH 2125 Calculus IV (3). The calculus of vector variables, including partial, differentiation and multiple integration, line integrals, Stokes’ theorem, and applications. Prerequisite: grade of C or better in MATH 2115 or permission of the Department Head. Offered in fall, spring, summer.
MATH 3120 Applied Mathematics (3). Ordinary differential equations, Fourier series, and Laplace transforms, with emphasis on the application to mechanical and electrical systems. Prerequisites: grades of C or better in MATH 2125 or 2110 and in PHYS 2120, 2121. MATH 3120 is required of all Physics majors. Offered on demand.
MATH 3130 Advanced Mathematica (3) (Formerly MATH 313). An in-depth treatment of the computer software “Mathematica” with emphasis on programming in the “Mathematica” language to solve selected problems. Prerequisites: grades of C or better in MATH 2110 and 3610, and COMP 2120, or permission of the Department Head. Offered in fall.
MATH 3210 Introduction to Number Theory (3) (Formerly MATH 321). Divisibility properties for the integers, the greatest common divisor, unique factorization, congruences, Diophantine equations, the Euler function, Wilson’s theorem, the Chinese remainder theorem, and other elementary properties of number. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered in fall.
MATH 3510 Intermediate Analysis (3) (Formerly MATH 351). A study of the foundations of real variable calculus, including the real numbers, limits, sequences, continuity, Bolzano-Weierstrass theorem, Heine-Borel theorem, intermediate-value theorem, and differentiability. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all Mathematics and Physics majors. Offered in spring and summer.
MATH 3610 Linear Algebra I (3) (Formerly MATH 361). Homogeneous and non-homogeneous systems, matrix algebra, determinants, vector spaces and subspaces, bases, orthogonal bases, linear transformations, and rank. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all Mathematics, Physics, and Computer Science majors. Offered in fall, spring, and summer.
MATH 3620 Linear Algebra II (3) (Formerly MATH 362). A continuation of MATH 3610. It is strongly recommended that 3610 and 3620 be taken sequentially. Topics include a further treatment of linear transformations, rank, eigenvalues, eigenvectors, and the spectral theorem. Prerequisite: grade of C or better in MATH 3610. Required of all Mathematics majors. Offered in spring.
MATH 3640 Abstract Algebra (3) (Formerly MATH 364). An introduction to properties of groups, rings, integral domains, and fields. Prerequisites: grades of C or better in MATH 1920 and 3210, or permission of Department Head. Required of all Mathematics majors. Offered in spring.
MATH 3710 Teaching Mathematics in the Secondary School (3) (Formerly MATH 371). Lectures, discussions, and reports on materials and methods used in the instruction of mathematics at the middle school and high school level. Clinical and field-based experiences which call for active participation by students are part of the course requirements. Required of all students seeking certification in Mathematics. Prerequisite: official admission to the Teacher Education Program. Offered in spring.
MATH 3810 Geometry (3) (Formerly MATH 381). A brief review of Euclidean geometry with further topics, including the non-Euclidean and projective geometries. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all teacher certification candidates in Mathematics. Offered in fall of odd numbered and summer of even-numbered years.
MATH 3900 Introduction to Numerical Analysis (3) (Formerly MATH 390). Errors, interpolation, approximations, numerical quadrature, solution of ordinary differential equations. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered on demand.
MATH 4310, 4320 Topology I, II (3, 3) (Formerly MATH 431, 432). Homeomorphisms, connectedness, compactness, metric spaces, normal spaces, Urysohn’s lemma, Tietze’s theorem, separation axioms, product topology, Hilbert space, quotient space, paracompactness, nets, and filters, with an introduction to homotopy theory. Prerequisites: grades of C or better in MATH 2110, and 3510, or permission of the Department Head. Offered on demand.
MATH 4410, 4420 Advanced Calculus I, II (3, 3) (Formerly MATH 441, 442). A variety of topics including functions of several variables; the algebra and topology of Euclidean n-space; differentials; extrema; the gradient; line, surface and volume integral; Stokes’ theorem; inverse mapping theorem; and manifolds. Prerequisites: grades of C or better in MATH 2110, 3510, and 3610, or permission of the Department Head. Mathematics majors must take this sequence or MATH 4640-4650 or STAT 4210-4220. MATH 4410 is offered in fall and 4420 in spring.
MATH 4500 Senior Project (3) (Formerly MATH 450). A comprehensive inquiry into the nature of mathematics . Emphasis is on written presentation of the subject matter. Required of all prospective graduating seniors in Mathematics. Prerequisite: senior standing. Offered in fall.
MATH 4510, 4520 Real Analysis I, II (3, 3) (Formerly MATH 451, 452). Set theory, algebra, and topology of the real numbers, continuous functions, uniform convergence, measure and integration theory, Lebesque measure and integrals, convergence theorem, L-spaces, Banach spaces, differentiation, Radon-Nikodym theorem, Fubini theorem. Prerequisite: grade of C or better in MATH 4420 or permission of the Department Head. Offered on demand.
MATH 4530, 4540 Complex Analysis I, II (3, 3) (Formerly MATH 453, 454). Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series, singularities, residue theory, analytic continuation, conformal mapping, Riemann surfaces, infinite products, and entire functions. Prerequisite: grade of C or better in MATH 442 or permission of the Department Head. MATH 4530 is offered in fall of odd-numbered years and 4540 is offered in spring of even-numbered years.
MATH 4560, 4570 Differential Equations I, II (3, 3) (Formerly MATH 456, 457). First- and second-order equations, general theory of linear nth-order differential equations, constant coefficient systems, variation of parameters, infinite series, singular solutions, asymptotic solutions, Green’s functions, stability, special functions, Laplace transform. Prerequisites: grades of C or better in MATH 3030 and 3620, or permission of the Department Head. MATH 4560 is offered in fall of even-numbered years and spring of odd-numbered years.
MATH 4640, 4650 Modern Algebra I, II (3, 3) (Formerly MATH 464, 465). Equivalence relations, mappings, groups, rings, fields, polynomial rings, modules, vector spaces, Galois theory. Prerequisites: grades of C or better in MATH 3210, 3620, and 3640, or permission of the Department Head. Mathematics majors must take this sequence or MATH 4410-4420 or STAT 4210-4220. MATH 4640 is offered in the fall and 4650 in the spring.
MATH 4724 Student Teaching of Mathematics in the Secondary Schools (9) (Formerly MATH 472S). A semester-long experience of supervised practice teaching, appropriately divided between middle school and high school. Required of all students seeking certification in teaching mathematics. Prerequisite: successful completion of all certification courses except EDCI 4705, which is taken concurrently. Offered on demand.
MATH 4730, 4740 Logic I, II (3, 3) (Formerly MATH 473, 474). Introduction to mathematical logic. Logic I is a survey of fundamental material including the statement calculus and the predicate calculus. Logic II is an introduction to Fuzzy Logic and Gödel’s Incompleteness Theorem. Prerequisite: grade of C or better in MATH 2110 or permission of the Department Head. Offered on demand.
MATH 4750 History of Mathematics (3) (Formerly MATH 475). The origin and development of mathematical ideas, beginning with geometry and algebra and continuing through selected topics in modern mathematics. Prerequisite: grade of C or better in MATH 2110 or permission of the Department Head. Offered in fall or even numbered and summer of odd-numbered years.
MATH 4900 Special Topics (3) (Formerly MATH 490). Special topics in mathematics to be offered with permission of the undergraduate mathematics curriculum committee in response to the preference and needs of the students. Repeatable to six hours. Prerequisite: permission of the Department Head. Offered in fall, spring, and summer.
Statistics (STAT)
STAT 1510, 1520 Introduction to Probability and Statistics I, II (3, 3). An overview of what statistics is and what statisticians do. Topics include basic concepts of probability, random variables and probability distributions, basic concepts of inference, linear regression and correlation, analysis of variance, and analysis of enumerative data. Prerequisite: permission of the Department Head. STAT 1510 is offered in fall and 1520 on demand.
STAT 3110, 3120 Probability and Statistics I, II (3, 3) (Formerly STAT 311, 312). Probability as a tool for inference: the axioms of probability, random variables and their probability distributions, multivariate probability distributions, functions of random variables, hypothesis testing, linear models and estimation by least squares, the general linear model, analysis of categorical data, and non-parametric statistics. Prerequisite: MATH 1920 or permission of the Department Head. STAT 3110 is required of all Computer Science majors. STAT 3110 is offered every semester; 3120 is offered only in the spring.
STAT 3700 Introduction to Statistical Computing and Data Management (3) (Formerly STAT 370). Components of digital computers, characteristics of magnetic storage devices, use of JCL and utility programs, concepts and techniques of research data management. Prerequisites: MATH 1920 and CS 222, or permission of the Department Head. Offered on demand.
STAT 4210 Statistical Methods I (3) (Formerly STAT 421). Approaches to the problems of description and goodness of fit; univariate location and scale; elvariate independence and correlation; comparison of independent or matched samples, involving categorical, discrete, or continuous data; non-parametric tests. Prerequisite: STAT 3120 or permission of the Department Head. All Mathematics majors must take the STAT 4210-4220 sequence or MATH 4410-4420 or MATH 4640-4650. Offered in fall.
STAT 4220 Statistical Methods II (3) (Formerly STAT 422). A continuation of STAT 4210. Topics include simple and multiple regression, analysis of variance and covariance, elements of experimental design and analysis, random effects models, simultaneous inference and the general linear model in matrix terms. Prerequisite: STAT 4210 or permission of the Department Head. Offered in spring.
Departmental Requirements 38 Semester Hours
For Bachelor of Science
Mathematics
The curriculum for a B.S. degree in Mathematics consists of a minimum of 120 semester hours, of which 42 must be at the 3000 or 4000 level. A minimum of 38 semester hours must be in Mathematics or Statistics, exclusive of MATH 1005, 1115, 1710, 1720, and 1730 with at least 27 of these being at the 3000 or 4000 level, exclusive of MATH 3710, 4724, and 4750. Note that Computer Science 3900 may be used to satisfy upper level course requirements for the major in Mathematics. The 38 hours in Mathematics are differentiated into a required core and an appropriate specialization. Further requirements include 12 hours (6 hours for teacher certification candidates) of Computer Science and 8 hours of Physics. Also it is strongly recommended that the student include related areas (RA’s) of interest in the program of study. Because of the very tight prerequisite structure, no major program in Mathematics should be started without first consulting a major advisor. No Mathematics or Statistics course in which a grade below C is earned will be counted towards meeting the Mathematics major core requirements.
The Mathematics core consists of a calculus sequence, an introduction to real analysis, courses in linear and abstract algebra, a sequence in either advanced calculus or modern algebra, and a senior project. A methods course in the teaching of mathematics is required for those who are certifying to teach. In addition to successfully completing 38 hours of course work (grade C or above), the major must pass a written comprehensive examination on the core requirements.
Students who minor in Mathematics must earn at least 23 or 26 semester hours: 11 or 14 semester hours of calculus depending on the sequence taken and a minimum of 12 semester hours of 3000 or 4000 level MATH or STAT courses, exclusive of MATH 3710, 4724, and 4750. Computer Science 3900 may be used to satisfy upper level course requirements for the minor in Mathematics.
Besides the general program where the recommended RA’s (related areas) are pre-medicine, pre-law, etc., there are four options of specialization.
a) The pure Mathematics option includes MATH 4310 and 4530, as well as both the sequences MATH 4410-4420 and 4640-4650 in the required core. The recommended RA’s include computer science, physics, and philosophy.
b) The applied Mathematics option includes MATH 3120, 4560, and 4570, as well as MATH 4410-4420 in the required core. The recommended RA’s include engineering, physics, computer science, and chemistry.
c) The statistics option allows the student to use STAT 4210-4220 to satisfy the sequence requirement. The recommended RA’s include pre-actuarial science, general business, sociology, and psychology.
d) The secondary mathematics teacher option includes COMP 3200, STAT 3110, and MATH 3810, 4410, 4420, and 4750 in the required core. Students seeking teacher certification must apply in writing to the College of Education, usually in the sophomore year. At the time of applying they must have a 2.75 cumulative grade point average and must have passed the Pre-Professional Skills Test (PPST) or the Computer-Based Academic Skills Assessments Test (CBT). Students who have previously earned a 21 on the ACT, 22 on the Enhanced ACT, or a combined 990 on the verbal and mathematics portions of the SAT are exempt from the PPST and the CBT. Formal admission to the Teacher Education Program is a prerequisite for enrolling in upper-division certification courses.
Students must pass PRAXIS II exam before they can enroll in student teaching. Students must complete nine semester hours of enhanced student teaching with an eight-week placement at the secondary level and a seven-week placement at the middle school level. Successful completion of the program results in licensure to teach grades 7-12. For a complete list of requirements for admission to and retention in the Teacher Education Program, see the College of Education section.
General Education Core
Communications (9 hours)
ENGL 1010, 1020 Freshman English I, II 6
(minimum grade of C in each)
COMM 2200 Public Speaking 3
Humanities and/or Fine Arts (9 hours)
ENGL 2110-2322 Sophomore Literature 3
Elective From approved list. 3
Elective From approved list. 3
Social and Behavioral Science (6 hours)
ECON 2010 Principles of Economics I 3
Elective From approved list. 3
History (6 hours)
HIST 2010 American History I 3
HIST 2020 American History II 3
Natural Science (8 hours)
PHYS 2110/2111 General Physics I 4
PHYS 2120/2111 General Physics II 4
Mathematics (3 hours)
MATH 1910 Calculus I, Alternative 4
(Minimum grade of C.)
Orientation (1 hour)
ASOR 1001 Orientation for Science Majors 1
(Teacher certification students should take EDCI 1010.)
--------------------------------------------------------------------------------
Total General Education Hours 42
Upper–division Admission
For admission into the upper-division program of the Mathematics major, students must complete all of the requirements listed above under General Education Core. In addition, they must have removed all high school deficiencies, passed all required remedial/developmental courses, earned a cumulative grade point average of at least 2.0 on college-level course work, and completed the Rising Junior Examination. They must also have earned a grade of C or better in MATH 1910, 1920 and 2110.
Major Core (27, 24 for teacher certification candidates)
MATH 3510 Intermediate Analysis 3
MATH 3610 Linear Algebra I 3
MATH 3620 Linear Algebra II 3
(Not required for teacher certification candidates)
MATH 3640 Abstract Algebra 3
MATH 4410, 4420, or Advanced Calculus I, II, or 6
MATH 4640, 4650, or Modern Algebra I, II or
STAT 4210, 4220 Statistical Methods I, II
(MATH 4410, 4420 required of teacher
certification candidates)
MATH 4500 Senior Project 3
ELECTIVES 6
(teacher certification candidates take STAT 3110 and MATH 3810)
Suggested courses in areas of specialization may be obtained by consulting the major advisor.
Professional Education Core (37)
Requirements for Teacher certification students, only.
PSYC 2420 Human Growth& Learning 3
EDCI 2010 History & Foundation of Education 3
EDCI 3870 Curriculum Development 3
EDSE 3330 Education of Exceptional Children 3
PSYC 3120 Measurement/Evaluation in Schools 3
EDAD 4000 Professional Rights and Responsibilities 3
EDRD 4910 Reading & Study in Secondary School 3
EDCI 4190 Technology in the Schools 2
MATH 4724 Student Teaching of Mathematics 9
EDCI 4705 Educational Seminar 3
MATH 3710 Teaching Mathematics in the Secondary Schools 3
Bachelor of Science Degree in Mathematics
Suggested Four-Year Plan
FRESHMAN YEAR
Fall Semester HR Spring Semester HR
*MATH 1910 4 MATH 1920 4
ENGL 1010 3 ENGL 1020 3
HIST 2010 3 HIST 2020 3
COMP 2100 3 COMP 2110 3
ASOR 1001 1 HUMANITIES ELECTIVE 3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
14
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
16
*MATH 1710 and/or 1720 must be taken prior to MATH 1910 if need is indicated.
SOPHOMORE YEAR
Fall Semester HR Spring Semester HR
MATH 2110 3 COMM 2200 3
ENGL 2010 3 HUMANITIES ELECTIVE 3
PHYS 2110, 2111 4 PHYS 2120, 2121 4
COMP 2120 3 ECON 2010 3
SOC SCI EL 3 ELECTIVE, ANY LEVEL 3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
16
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
16
JUNIOR YEAR
Fall Semester HR Spring Semester HR
MATH 3610 3 MATH 3620 4
COMP 3200 3 MATH 3510 3
ELECTIVES, ANY LEVEL 3 MATH 3640 3
HUMANITIES ELECTIVE 3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
15
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
15
SENIOR YEAR
FALL SEMSTER HR SPRING SEMESTER HR
MATH 4410 or 4640 or MATH 4420 or 4650 or
STAT 4210 3 STAT 4220 3
MATH 4500 3 MATH ELECTIVE 3000/4000 3
MATH ELECTIVE, 3000/4000 3 ELECTIVES, 3000/4000 8
ELECTIVES, 3000/4000 5
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
14
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
14
Bachelor of Science Degree in Mathematics
With Teacher Certification
Licensure for Grades 7-12
Suggested Four-Year Plan (122)
FRESHMAN YEAR
Fall Semester HR Spring Semester HR
*MATH 1910 4 MATH 1920 4
ENGL 1010 3 MATH 1005 1
HIST 2010 3 ENGL 1020 3
HUMANITIES ELECTIVE 3 HIST 2020 3
EDCI 1001 1 COMP 2100 3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
14
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
14
*MATH 1710 and/or 1720 must be taken prior to MATH 1910 if need is indicated.
SOPHOMORE YEAR
Fall Semester HR Spring Semester HR
MATH 2110 3 COMM 2200 3
ENGL 2010 3 HUMANITIES ELECTIVE 3
PHYS 2110, 2111 4 PHYS 2120, 2121 4
PSYC 2420 3 ECON 2010 3
SOC SCI EL 3 EDCI 2010 3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
16
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
16
JUNIOR YEAR
Fall Semester HR Spring Semester HR
MATH 3510 3 MATH 3640 3
MATH 3610 3 MATH 4410 3
PSYC 3120 3 MATH 3810 3
STAT 3110 3 MATH 4750 3
EDAD 4910 3 EDSE 3330 3
EDCI 3870 3 EDCI 4190 2
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
18
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
17
SENIOR YEAR
FALL SEMSTER HR SPRING SEMESTER HR
COMP 3200 3 MATH 4724 9
MATH 4420 3 EDCI 4705 3
MATH 4500 3
MATH 3710 3
EDAD 4000 3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
15
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
12
Course Descriptions
Mathematics (MATH)
MATH 1001 The Mathematics of Drugs and Solutions (1) (Formerly MATH 110). A course in measurements, calculations, and related topics for those entering the nursing profession. Calculations include the metric apothecary and home-type units, as well as determining IV rates, solution strengths, and miscellaneous procedures. Prerequisites: two years of high school algebra or one year of algebra and one year of geometry, or the equivalent. Course cannot be applied to satisfying the University mathematics requirement. Offered in fall and spring.
MATH 1005 Mathematics Education Orientation (1) (Formerly MATH 192). An introduction to the Mathematics teacher education program, including field experience. Prerequisite: interest in becoming a mathematics teacher. Offered in spring.
MATH 1013 Contemporary Mathematics (3). An Introduction to the mathematics used in our society. It includes elements of mathematical thought, inductive and deductive reasoning, and problem solving. Some of the topics included are graphics, counting techniques, number sequences, probability and statistics. This course satisfies the general education mathematics requirement. Prerequisites: Two years high school algebra or the equivalent, or one year of high school algebra and one year geometry or the equivalent. Offered in the fall, spring, and summer.
MATH 1110 College Algebra I (3). Graphs, relations, functions, inequalities, polynomials, exponents, radicals, logarithms, and exponential functions. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one year of geometry, or the equivalent. Offered in fall, spring, and summer.
MATH 1111 Honors College Algebra I (3). The Honors version of MATH 1110. Enrollment is limited to members of the University Honors College. Offered in fall.
MATH 1115 Fundamentals of Problem-Solving (1) (Formerly MATH 191). An introduction to Polya theories with emphasis on solving problems using mathematical methods. Prerequisite: 3 semester hours of college-level mathematics or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1120 College Algebra II (3). Rational functions, conic sections, systems of equations and inequalities, matrices and determinants, and an introduction to discrete mathematics. Prerequisite: grade of C or better in MATH 1110 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1121 Honors College Algebra II (3). The Honors version of MATH 1120. Enrollment is limited to members of the University Honors College. Offered on demand.
MATH 1140 Analytic Geometry and Trigonometry (3) (Formerly MATH 114). A survey of analytic geometry and trigonometry, including conic sections, connections among right triangle ratios, variation, periodic and circular functions, and the use of appropriate calculators and computers. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one of geometry, or the equivalent. Offered in fall and spring.
MATH 1410, 1420 Structure of the Number System I, II (3, 3). Set theory; relations; functions; inverses; order properties; systems of numeration; rational and irrational numbers; elementary number theory; mathematical systems; algorithms for the fundamental operations on whole numbers, integers, fractions, decimals, percent, ratio and proportion; equations; problem-solving; measurement in the metric system; elements of algebra; plane and solid geometry; elementary statistics. Prerequisite: For MATH 1410: Two years of high school algebra or the equivalent or one year high school algebra and one year geometry or the equivalent. For MATH 1420: MATH 1410. MATH 1410 Offered in fall, spring, and summer. MATH 1420 Offered in fall and spring.
MATH 1610 Introduction to Discrete Mathematics (3). A study of sets, relations and functions, mathematical induction, Boolean algebra and Boolean functions. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one of geometry, or the equivalent. Offered on demand.
MATH 1710 Precalculus Mathematics I (3). A course which with MATH 1720 provides the student with the foundation necessary to enter the calculus sequence. The topics include the study of polynomial, rational, exponential and logarithmic functions, and matrices. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one year of geometry, or the equivalent. Offered in fall, spring, and summer.
MATH 1720 Precalculus Mathematics II (3). A continuation of MATH 1710. Topics include right triangle trigonometry, trigonometric functions, analytic geometry, conic sections, sequences, and notation. Prerequisite: grade of C or better in MATH 1710 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1730 Precalculus Mathematics, Alternate (3). Integrated college algebra and trigonometry. This course provides the student with the background necessary to enter the calculus sequence. Topics include polynomials; rational functions; exponential, logarithmic, and trigonometric functions; analytic geometry; and conic sections. Prerequisites: high school algebra II, geometry, and trigonometry, or the equivalent. Offered in fall and spring.
MATH 1830 Basic Calculus I (3). An introduction to the basic concepts of differential and integral calculus, with applications oriented towards economics, business, and the social sciences. Prerequisite: grade of C or better in MATH 1110 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1910 Calculus I, Alternate (4) (Formerly MATH 1910). Part of the sequence MATH 1910, 1920 recommended for Mathematics, Physics, Chemistry, and Biology majors. Topics include functions, graphs, limits, derivatives with applications, and the definite integral with applications. Prerequisite: grade of C or better in MATH 1720 or 1730 or permission of the Department Head. Offered in fall.
MATH 1915 Calculus and Analytical Geometry (4). Part of the sequence MATH 1915, 1925, 2115, 2125, which emphasizes application to the physical sciences. Topics include functions, graphs, limits, derivatives, the definite integral, and rational functions including applications. Prerequisite: grade of C or better in MATH 1720 or 1730 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1920 Calculus II, Alternate (4). Study of derivatives and integrals of the trigonometric, logarithmic, and exponential functions, techniques of integration, sequences, and series. Course is part of the series MATH 1910, 1920, 2110, recommended for all Mathematics, Physics, Chemistry, and Biology majors. Prerequisite: grade of C or better in MATH 1910 or permission of the Department Head. Offered in spring.
MATH 1925 Calculus II (4). Further applications of definite integral, derivatives and integrals of transcendental functions, techniques of integration, and polar coordinates. Prerequisite: grade of C or better in MATH 1910 or 1915 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 2110 Calculus III, Alternate (3). Vector functions, three- dimensional space, partial derivatives, multiple integrals, line integrals, and applications. Part of the sequence MATH 1910, 1920, and 2110 recommended for all Mathematics, Physics, Biology, and Chemistry majors. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered in fall.
MATH 2115 Calculus III (3). Infinite sequences and series, vectors in two- and three-dimensional space, the calculus of a vector function, and applications. Prerequisite: grade of C or better in MATH 1925 or permission of the Department Head. Offered in fall, spring, summer.
MATH 2125 Calculus IV (3). The calculus of vector variables, including partial, differentiation and multiple integration, line integrals, Stokes’ theorem, and applications. Prerequisite: grade of C or better in MATH 2115 or permission of the Department Head. Offered in fall, spring, summer.
MATH 3120 Applied Mathematics (3). Ordinary differential equations, Fourier series, and Laplace transforms, with emphasis on the application to mechanical and electrical systems. Prerequisites: grades of C or better in MATH 2125 or 2110 and in PHYS 2120, 2121. MATH 3120 is required of all Physics majors. Offered on demand.
MATH 3130 Advanced Mathematica (3) (Formerly MATH 313). An in-depth treatment of the computer software “Mathematica” with emphasis on programming in the “Mathematica” language to solve selected problems. Prerequisites: grades of C or better in MATH 2110 and 3610, and COMP 2120, or permission of the Department Head. Offered in fall.
MATH 3210 Introduction to Number Theory (3) (Formerly MATH 321). Divisibility properties for the integers, the greatest common divisor, unique factorization, congruences, Diophantine equations, the Euler function, Wilson’s theorem, the Chinese remainder theorem, and other elementary properties of number. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered in fall.
MATH 3510 Intermediate Analysis (3) (Formerly MATH 351). A study of the foundations of real variable calculus, including the real numbers, limits, sequences, continuity, Bolzano-Weierstrass theorem, Heine-Borel theorem, intermediate-value theorem, and differentiability. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all Mathematics and Physics majors. Offered in spring and summer.
MATH 3610 Linear Algebra I (3) (Formerly MATH 361). Homogeneous and non-homogeneous systems, matrix algebra, determinants, vector spaces and subspaces, bases, orthogonal bases, linear transformations, and rank. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all Mathematics, Physics, and Computer Science majors. Offered in fall, spring, and summer.
MATH 3620 Linear Algebra II (3) (Formerly MATH 362). A continuation of MATH 3610. It is strongly recommended that 3610 and 3620 be taken sequentially. Topics include a further treatment of linear transformations, rank, eigenvalues, eigenvectors, and the spectral theorem. Prerequisite: grade of C or better in MATH 3610. Required of all Mathematics majors. Offered in spring.
MATH 3640 Abstract Algebra (3) (Formerly MATH 364). An introduction to properties of groups, rings, integral domains, and fields. Prerequisites: grades of C or better in MATH 1920 and 3210, or permission of Department Head. Required of all Mathematics majors. Offered in spring.
MATH 3710 Teaching Mathematics in the Secondary School (3) (Formerly MATH 371). Lectures, discussions, and reports on materials and methods used in the instruction of mathematics at the middle school and high school level. Clinical and field-based experiences which call for active participation by students are part of the course requirements. Required of all students seeking certification in Mathematics. Prerequisite: official admission to the Teacher Education Program. Offered in spring.
MATH 3810 Geometry (3) (Formerly MATH 381). A brief review of Euclidean geometry with further topics, including the non-Euclidean and projective geometries. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all teacher certification candidates in Mathematics. Offered in fall of odd numbered and summer of even-numbered years.
MATH 3900 Introduction to Numerical Analysis (3) (Formerly MATH 390). Errors, interpolation, approximations, numerical quadrature, solution of ordinary differential equations. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered on demand.
MATH 4310, 4320 Topology I, II (3, 3) (Formerly MATH 431, 432). Homeomorphisms, connectedness, compactness, metric spaces, normal spaces, Urysohn’s lemma, Tietze’s theorem, separation axioms, product topology, Hilbert space, quotient space, paracompactness, nets, and filters, with an introduction to homotopy theory. Prerequisites: grades of C or better in MATH 2110, and 3510, or permission of the Department Head. Offered on demand.
MATH 4410, 4420 Advanced Calculus I, II (3, 3) (Formerly MATH 441, 442). A variety of topics including functions of several variables; the algebra and topology of Euclidean n-space; differentials; extrema; the gradient; line, surface and volume integral; Stokes’ theorem; inverse mapping theorem; and manifolds. Prerequisites: grades of C or better in MATH 2110, 3510, and 3610, or permission of the Department Head. Mathematics majors must take this sequence or MATH 4640-4650 or STAT 4210-4220. MATH 4410 is offered in fall and 4420 in spring.
MATH 4500 Senior Project (3) (Formerly MATH 450). A comprehensive inquiry into the nature of mathematics . Emphasis is on written presentation of the subject matter. Required of all prospective graduating seniors in Mathematics. Prerequisite: senior standing. Offered in fall.
MATH 4510, 4520 Real Analysis I, II (3, 3) (Formerly MATH 451, 452). Set theory, algebra, and topology of the real numbers, continuous functions, uniform convergence, measure and integration theory, Lebesque measure and integrals, convergence theorem, L-spaces, Banach spaces, differentiation, Radon-Nikodym theorem, Fubini theorem. Prerequisite: grade of C or better in MATH 4420 or permission of the Department Head. Offered on demand.
MATH 4530, 4540 Complex Analysis I, II (3, 3) (Formerly MATH 453, 454). Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series, singularities, residue theory, analytic continuation, conformal mapping, Riemann surfaces, infinite products, and entire functions. Prerequisite: grade of C or better in MATH 442 or permission of the Department Head. MATH 4530 is offered in fall of odd-numbered years and 4540 is offered in spring of even-numbered years.
MATH 4560, 4570 Differential Equations I, II (3, 3) (Formerly MATH 456, 457). First- and second-order equations, general theory of linear nth-order differential equations, constant coefficient systems, variation of parameters, infinite series, singular solutions, asymptotic solutions, Green’s functions, stability, special functions, Laplace transform. Prerequisites: grades of C or better in MATH 3030 and 3620, or permission of the Department Head. MATH 4560 is offered in fall of even-numbered years and spring of odd-numbered years.
MATH 4640, 4650 Modern Algebra I, II (3, 3) (Formerly MATH 464, 465). Equivalence relations, mappings, groups, rings, fields, polynomial rings, modules, vector spaces, Galois theory. Prerequisites: grades of C or better in MATH 3210, 3620, and 3640, or permission of the Department Head. Mathematics majors must take this sequence or MATH 4410-4420 or STAT 4210-4220. MATH 4640 is offered in the fall and 4650 in the spring.
MATH 4724 Student Teaching of Mathematics in the Secondary Schools (9) (Formerly MATH 472S). A semester-long experience of supervised practice teaching, appropriately divided between middle school and high school. Required of all students seeking certification in teaching mathematics. Prerequisite: successful completion of all certification courses except EDCI 4705, which is taken concurrently. Offered on demand.
MATH 4730, 4740 Logic I, II (3, 3) (Formerly MATH 473, 474). Introduction to mathematical logic. Logic I is a survey of fundamental material including the statement calculus and the predicate calculus. Logic II is an introduction to Fuzzy Logic and Gödel’s Incompleteness Theorem. Prerequisite: grade of C or better in MATH 2110 or permission of the Department Head. Offered on demand.
MATH 4750 History of Mathematics (3) (Formerly MATH 475). The origin and development of mathematical ideas, beginning with geometry and algebra and continuing through selected topics in modern mathematics. Prerequisite: grade of C or better in MATH 2110 or permission of the Department Head. Offered in fall or even numbered and summer of odd-numbered years.
MATH 4900 Special Topics (3) (Formerly MATH 490). Special topics in mathematics to be offered with permission of the undergraduate mathematics curriculum committee in response to the preference and needs of the students. Repeatable to six hours. Prerequisite: permission of the Department Head. Offered in fall, spring, and summer.
Statistics (STAT)
STAT 1510, 1520 Introduction to Probability and Statistics I, II (3, 3). An overview of what statistics is and what statisticians do. Topics include basic concepts of probability, random variables and probability distributions, basic concepts of inference, linear regression and correlation, analysis of variance, and analysis of enumerative data. Prerequisite: permission of the Department Head. STAT 1510 is offered in fall and 1520 on demand.
STAT 3110, 3120 Probability and Statistics I, II (3, 3) (Formerly STAT 311, 312). Probability as a tool for inference: the axioms of probability, random variables and their probability distributions, multivariate probability distributions, functions of random variables, hypothesis testing, linear models and estimation by least squares, the general linear model, analysis of categorical data, and non-parametric statistics. Prerequisite: MATH 1920 or permission of the Department Head. STAT 3110 is required of all Computer Science majors. STAT 3110 is offered every semester; 3120 is offered only in the spring.
STAT 3700 Introduction to Statistical Computing and Data Management (3) (Formerly STAT 370). Components of digital computers, characteristics of magnetic storage devices, use of JCL and utility programs, concepts and techniques of research data management. Prerequisites: MATH 1920 and CS 222, or permission of the Department Head. Offered on demand.
STAT 4210 Statistical Methods I (3) (Formerly STAT 421). Approaches to the problems of description and goodness of fit; univariate location and scale; elvariate independence and correlation; comparison of independent or matched samples, involving categorical, discrete, or continuous data; non-parametric tests. Prerequisite: STAT 3120 or permission of the Department Head. All Mathematics majors must take the STAT 4210-4220 sequence or MATH 4410-4420 or MATH 4640-4650. Offered in fall.
STAT 4220 Statistical Methods II (3) (Formerly STAT 422). A continuation of STAT 4210. Topics include simple and multiple regression, analysis of variance and covariance, elements of experimental design and analysis, random effects models, simultaneous inference and the general linear model in matrix terms. Prerequisite: STAT 4210 or permission of the Department Head. Offered in spring.
General Statement: The objectives of the Mathematics Program are (1) to provide training to enable graduates to be employed by any of a number of private industries, government agencies, foundations, and institutions requiring high-level quantitative skills and a highly developed ability to think critically and logically; (2) to provide training to enable graduates to enter graduate school in mathematics or related areas; (3) to provide training to enable graduates to assume careers as teachers of mathematics in secondary schools; (4) to develop proficiency in basic mathematical operations and develop skills in the use of formulas for the solution of problems; (5) to provide science and engineering majors the mathematical skills required by their various programs of study.
Departmental Requirements 38 Semester Hours
For Bachelor of Science
Mathematics
The curriculum for a B.S. degree in Mathematics consists of a minimum of 120 semester hours, of which 42 must be at the 3000 or 4000 level. A minimum of 38 semester hours must be in Mathematics or Statistics, exclusive of MATH 1005, 1115, 1710, 1720, and 1730 with at least 27 of these being at the 3000 or 4000 level, exclusive of MATH 3710, 4724, and 4750. Note that Computer Science 3900 may be used to satisfy upper level course requirements for the major in Mathematics. The 38 hours in Mathematics are differentiated into a required core and an appropriate specialization. Further requirements include 12 hours (6 hours for teacher certification candidates) of Computer Science and 8 hours of Physics. Also it is strongly recommended that the student include related areas (RA ’ s) of interest in the program of study. Because of the very tight prerequisite structure, no major program in Mathematics should be started without first consulting a major advisor. No Mathematics or Statistics course in which a grade below C is earned will be counted towards meeting the Mathematics major core requirements.
The Mathematics core consists of a calculus sequence, an introduction to real analysis, courses in linear and abstract algebra, a sequence in either advanced calculus or modern algebra, and a senior project. A methods course in the teaching of mathematics is required for those who are certifying to teach. In addition to successfully completing 38 hours of course work (grade C or above), the major must pass a written comprehensive examination on the core requirements.
Students who minor in Mathematics must earn at least 23 or 26 semester hours: 11 or 14 semester hours of calculus depending on the sequence taken and a minimum of 12 semester hours of 3000 or 4000 level MATH or STAT courses, exclusive of MATH 3710, 4724, and 4750. Computer Science 3900 may be used to satisfy upper level course requirements for the minor in Mathematics.
Besides the general program where the recommended RA ’ s (related areas) are pre-medicine, pre-law, etc., there are four options of specialization.
| a) | The pure Mathematics option includes MATH 4310 and 4530, as well as both the sequences MATH 4410-4420 and 4640-4650 in the required core. The recommended RA ’ s include computer science, physics, and philosophy. |
| b) | The applied Mathematics option includes MATH 3120, 4560, and 4570, as well as MATH 4410-4420 in the required core. The recommended RA ’ s include engineering, physics, computer science, and chemistry. |
| c) | The statistics option allows the student to use STAT 4210-4220 to satisfy the sequence requirement. The recommended RA ’ s include pre-actuarial science, general business, sociology, and psychology. |
| d) | The secondary mathematics teacher option includes COMP 3200, STAT 3110, and MATH 3810, 4410, 4420, and 4750 in the required core. Students seeking teacher certification must apply in writing to the College of Education, usually in the sophomore year. At the time of applying they must have a 2.75 cumulative grade point average and must have passed the Pre-Professional Skills Test (PPST) or the Computer-Based Academic Skills Assessments Test (CBT). Students who have previously earned a 21 on the ACT, 22 on the Enhanced ACT, or a combined 990 on the verbal and mathematics portions of the SAT are exempt from the PPST and the CBT. Formal admission to the Teacher Education Program is a prerequisite for enrolling in upper-division certification courses. |
Students must pass PRAXIS II exam before they can enroll in student teaching. Students must complete nine semester hours of enhanced student teaching with an eight-week placement at the secondary level and a seven-week placement at the middle school level. Successful completion of the program results in licensure to teach grades 7-12. For a complete list of requirements for admission to and retention in the Teacher Education Program, see the College of Education section.
General Education Core
Communications (9 hours)
ENGL 1010, 1020 Freshman English I, II 6
(minimum grade of C in each)
COMM 2200 Public Speaking 3
Humanities and/or Fine Arts (9 hours)
ENGL 2110-2322 Sophomore Literature 3
Elective From approved list. 3
Elective From approved list. 3
Social and Behavioral Science (6 hours)
ECON 2010 Principles of Economics I 3
Elective From approved list. 3
History (6 hours)
HIST 2010 American History I 3
HIST 2020 American History II 3
Natural Science (8 hours)
PHYS 2110/2111 General Physics I 4
PHYS 2120/2111 General Physics II 4
Mathematics (3 hours)
MATH 1910 Calculus I, Alternative 4
(Minimum grade of C.)
Orientation (1 hour)
ASOR 1001 Orientation for Science Majors 1
(Teacher certification students should take EDCI 1010.)
Total General Education Hours 42
Upper – division Admission
For admission into the upper-division program of the Mathematics major, students must complete all of the requirements listed above under General Education Core. In addition, they must have removed all high school deficiencies, passed all required remedial/developmental courses, earned a cumulative grade point average of at least 2.0 on college-level course work, and completed the Rising Junior Examination. They must also have earned a grade of C or better in MATH 1910, 1920 and 2110.
Major Core (27, 24 for teacher certification candidates)
MATH 3510 Intermediate Analysis 3
MATH 3610 Linear Algebra I 3
MATH 3620 Linear Algebra II 3
(Not required for teacher
certification candidates)
MATH 3640 Abstract Algebra 3
MATH 4410, 4420, or Advanced Calculus I, II, or 6
MATH 4640, 4650, or Modern Algebra I, II or
STAT 4210, 4220 Statistical Methods I, II
(MATH 4410, 4420 required of teacher
certification candidates)
MATH 4500 Senior Project 3
ELECTIVES 6
(teacher certification candidates take
STAT 3110 and MATH 3810)
Suggested courses in areas of specialization may be obtained by consulting the major advisor.
Professional Education Core (37)
Requirements for Teacher certification students, only.
PSYC 2420 Human Growth& Learning 3
EDCI 2010 History & Foundation of Education 3
EDCI 3870 Curriculum Development 3
EDSE 3330 Education of Exceptional Children 3
PSYC 3120 Measurement/Evaluation in Schools 3
EDAD 4000 Professional Rights and Responsibilities 3
EDRD 4910 Reading & Study in Secondary School 3
EDCI 4190 Technology in the Schools 2
MATH 4724 Student Teaching of Mathematics 9
EDCI 4705 Educational Seminar 3
MATH 3710 Teaching Mathematics in the Secondary Schools 3
Bachelor of Science Degree in Mathematics
Suggested Four-Year Plan
FRESHMAN YEAR
| Fall Semester | HR | Spring Semester | HR |
| *MATH 1910 | 4 | MATH 1920 | 4 |
| ENGL 1010 | 3 | ENGL 1020 | 3 |
| HIST 2010 | 3 | HIST 2020 | 3 |
| COMP 2100 | 3 | COMP 2110 | 3 |
| ASOR 1001 | 1 | HUMANITIES ELECTIVE | 3 |
|
|
14 |
|
16 |
*MATH 1710 and/or 1720 must be taken prior to MATH 1910 if need is indicated.
SOPHOMORE YEAR
| Fall Semester | HR | Spring Semester | HR |
| MATH 2110 | 3 | COMM 2200 | 3 |
| ENGL 2010 | 3 | HUMANITIES ELECTIVE | 3 |
| PHYS 2110, 2111 | 4 | PHYS 2120, 2121 | 4 |
| COMP 2120 | 3 | ECON 2010 | 3 |
| SOC SCI EL | 3 | ELECTIVE, ANY LEVEL | 3 |
|
|
16 |
|
16 |
JUNIOR YEAR
| Fall Semester | HR | Spring Semester | HR |
| MATH 3610 | 3 | MATH 3620 | 4 |
| COMP 3200 | 3 | MATH 3510 | 3 |
| ELECTIVES, ANY LEVEL | 3 | MATH 3640 | 3 |
| HUMANITIES ELECTIVE | 3 | ||
|
|
15 |
|
15 |
SENIOR YEAR
| FALL SEMSTER | HR | SPRING SEMESTER | HR |
| MATH 4410 or 4640 or | MATH 4420 or 4650 or | ||
| STAT 4210 | 3 | STAT 4220 | 3 |
| MATH 4500 | 3 | MATH ELECTIVE 3000/4000 | 3 |
| MATH ELECTIVE, 3000/4000 | 3 | ELECTIVES, 3000/4000 | 8 |
| ELECTIVES, 3000/4000 | 5 | ||
|
|
14 |
|
14 |
Bachelor of Science Degree in Mathematics
With Teacher Certification
Licensure for Grades 7-12
Suggested Four-Year Plan (122)
FRESHMAN YEAR
| Fall Semester | HR | Spring Semester | HR |
| *MATH 1910 | 4 | MATH 1920 | 4 |
| ENGL 1010 | 3 | MATH 1005 | 1 |
| HIST 2010 | 3 | ENGL 1020 | 3 |
| HUMANITIES ELECTIVE | 3 | HIST 2020 | 3 |
| EDCI 1001 | 1 | COMP 2100 | 3 |
|
|
14 |
|
14 |
*MATH 1710 and/or 1720 must be taken prior to MATH 1910 if need is indicated.
SOPHOMORE YEAR
| Fall Semester | HR | Spring Semester | HR |
| MATH 2110 | 3 | COMM 2200 | 3 |
| ENGL 2010 | 3 | HUMANITIES ELECTIVE | 3 |
| PHYS 2110, 2111 | 4 | PHYS 2120, 2121 | 4 |
| PSYC 2420 | 3 | ECON 2010 | 3 |
| SOC SCI EL | 3 | EDCI 2010 | 3 |
|
|
16 |
|
16 |
JUNIOR YEAR
| Fall Semester | HR | Spring Semester | HR |
| MATH 3510 | 3 | MATH 3640 | 3 |
| MATH 3610 | 3 | MATH 4410 | 3 |
| PSYC 3120 | 3 | MATH 3810 | 3 |
| STAT 3110 | 3 | MATH 4750 | 3 |
| EDAD 4910 | 3 | EDSE 3330 | 3 |
| EDCI 3870 | 3 | EDCI 4190 | 2 |
|
|
18 |
|
17 |
SENIOR YEAR
| FALL SEMSTER | HR | SPRING SEMESTER | HR |
| COMP 3200 | 3 | MATH 4724 | 9 |
| MATH 4420 | 3 | EDCI 4705 | 3 |
| MATH 4500 | 3 | ||
| MATH 3710 | 3 | ||
| EDAD 4000 | 3 | ||
|
|
15 |
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Course Descriptions
Mathematics (MATH)
MATH 1001 The Mathematics of Drugs and Solutions (1) (Formerly MATH 110). A course in measurements, calculations, and related topics for those entering the nursing profession. Calculations include the metric apothecary and home-type units, as well as determining IV rates, solution strengths, and miscellaneous procedures. Prerequisites: two years of high school algebra or one year of algebra and one year of geometry, or the equivalent. Course cannot be applied to satisfying the University mathematics requirement. Offered in fall and spring.
MATH 1005 Mathematics Education Orientation (1) (Formerly MATH 192). An introduction to the Mathematics teacher education program, including field experience. Prerequisite: interest in becoming a mathematics teacher. Offered in spring.
MATH 1013 Contemporary Mathematics (3). An Introduction to the mathematics used in our society. It includes elements of mathematical thought, inductive and deductive reasoning, and problem solving. Some of the topics included are graphics, counting techniques, number sequences, probability and statistics. This course satisfies the general education mathematics requirement. Prerequisites: Two years high school algebra or the equivalent, or one year of high school algebra and one year geometry or the equivalent. Offered in the fall, spring, and summer.
MATH 1110 College Algebra I (3). Graphs, relations, functions, inequalities, polynomials, exponents, radicals, logarithms, and exponential functions. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one year of geometry, or the equivalent. Offered in fall, spring, and summer.
MATH 1111 Honors College Algebra I (3). The Honors version of MATH 1110. Enrollment is limited to members of the University Honors Program. Offered in fall.
MATH 1115 Fundamentals of Problem-Solving (1) (Formerly MATH 191). An introduction to Polya theories with emphasis on solving problems using mathematical methods. Prerequisite: 3 semester hours of college-level mathematics or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1120 College Algebra II (3). Rational functions, conic sections, systems of equations and inequalities, matrices and determinants, and an introduction to discrete mathematics. Prerequisite: grade of C or better in MATH 1110 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1121 Honors College Algebra II (3). The Honors version of MATH 1120. Enrollment is limited to members of the University Honors Program. Offered on demand.
MATH 1140 Analytic Geometry and Trigonometry (3) (Formerly MATH 114). A survey of analytic geometry and trigonometry, including conic sections, connections among right triangle ratios, variation, periodic and circular functions, and the use of appropriate calculators and computers. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one of geometry, or the equivalent. Offered in fall and spring.
MATH 1410, 1420 Structure of the Number System I, II (3, 3). Set theory; relations; functions; inverses; order properties; systems of numeration; rational and irrational numbers; elementary number theory; mathematical systems; algorithms for the fundamental operations on whole numbers, integers, fractions, decimals, percent, ratio and proportion; equations; problem-solving; measurement in the metric system; elements of algebra; plane and solid geometry; elementary statistics. Prerequisite: For MATH 1410: Two years of high school algebra or the equivalent or one year high school algebra and one year geometry or the equivalent. For MATH 1420: MATH 1410. MATH 1410 Offered in fall, spring, and summer. MATH 1420 Offered in fall and spring.
MATH 1610 Introduction to Discrete Mathematics (3). A study of sets, relations and functions, mathematical induction, Boolean algebra and Boolean functions. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one of geometry, or the equivalent. Offered on demand.
MATH 1710 Precalculus Mathematics I (3). A course which with MATH 1720 provides the student with the foundation necessary to enter the calculus sequence. The topics include the study of polynomial, rational, exponential and logarithmic functions, and matrices. Prerequisites: two years of high school algebra or the equivalent, or one year of high school algebra and one year of geometry, or the equivalent. Offered in fall, spring, and summer.
MATH 1720 Precalculus Mathematics II (3). A continuation of MATH 1710. Topics include right triangle trigonometry, trigonometric functions, analytic geometry, conic sections, sequences, and notation. Prerequisite: grade of C or better in MATH 1710 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1730 Precalculus Mathematics, Alternate (3). Integrated college algebra and trigonometry. This course provides the student with the background necessary to enter the calculus sequence. Topics include polynomials; rational functions; exponential, logarithmic, and trigonometric functions; analytic geometry; and conic sections. Prerequisites: high school algebra II, geometry, and trigonometry, or the equivalent. Offered in fall and spring.
MATH 1830 Basic Calculus I (3). An introduction to the basic concepts of differential and integral calculus, with applications oriented towards economics, business, and the social sciences. Prerequisite: grade of C or better in MATH 1110 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1910 Calculus I, Alternate (4) (Formerly MATH 1910). Part of the sequence MATH 1910, 1920 recommended for Mathematics, Physics, Chemistry, and Biology majors. Topics include functions, graphs, limits, derivatives with applications, and the definite integral with applications. Prerequisite: grade of C or better in MATH 1720 or 1730 or permission of the Department Head. Offered in fall.
MATH 1915 Calculus and Analytical Geometry (4). Part of the sequence MATH 1915, 1925, 2115, 2125, which emphasizes application to the physical sciences. Topics include functions, graphs, limits, derivatives, the definite integral, and rational functions including applications. Prerequisite: grade of C or better in MATH 1720 or 1730 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 1920 Calculus II, Alternate (4). Study of derivatives and integrals of the trigonometric, logarithmic, and exponential functions, techniques of integration, sequences, and series. Course is part of the series MATH 1910, 1920, 2110, recommended for all Mathematics, Physics, Chemistry, and Biology majors. Prerequisite: grade of C or better in MATH 1910 or permission of the Department Head. Offered in spring.
MATH 1925 Calculus II (4). Further applications of definite integral, derivatives and integrals of transcendental functions, techniques of integration, and polar coordinates. Prerequisite: grade of C or better in MATH 1910 or 1915 or permission of the Department Head. Offered in fall, spring, and summer.
MATH 2110 Calculus III, Alternate (3). Vector functions, three- dimensional space, partial derivatives, multiple integrals, line integrals, and applications. Part of the sequence MATH 1910, 1920, and 2110 recommended for all Mathematics, Physics, Biology, and Chemistry majors. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered in fall.
MATH 2115 Calculus III (3). Infinite sequences and series, vectors in two- and three-dimensional space, the calculus of a vector function, and applications. Prerequisite: grade of C or better in MATH 1925 or permission of the Department Head. Offered in fall, spring, summer.
MATH 2125 Calculus IV (3). The calculus of vector variables, including partial, differentiation and multiple integration, line integrals, Stokes ’ theorem, and applications. Prerequisite: grade of C or better in MATH 2115 or permission of the Department Head. Offered in fall, spring, summer.
MATH 3120 Applied Mathematics (3). Ordinary differential equations, Fourier series, and Laplace transforms, with emphasis on the application to mechanical and electrical systems. Prerequisites: grades of C or better in MATH 2125 or 2110 and in PHYS 2120, 2121. MATH 3120 is required of all Physics majors. Offered on demand.
MATH 3130 Advanced Mathematica (3) (Formerly MATH 313). An in-depth treatment of the computer software “Mathematica” with emphasis on programming in the “Mathematica” language to solve selected problems. Prerequisites: grades of C or better in MATH 2110 and 3610, and COMP 2120, or permission of the Department Head. Offered in fall.
MATH 3210 Introduction to Number Theory (3) (Formerly MATH 321). Divisibility properties for the integers, the greatest common divisor, unique factorization, congruences, Diophantine equations, the Euler function, Wilson ’ s theorem, the Chinese remainder theorem, and other elementary properties of number. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered in fall.
MATH 3510 Intermediate Analysis (3) (Formerly MATH 351). A study of the foundations of real variable calculus, including the real numbers, limits, sequences, continuity, Bolzano-Weierstrass theorem, Heine-Borel theorem, intermediate-value theorem, and differentiability. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all Mathematics and Physics majors. Offered in spring and summer.
MATH 3610 Linear Algebra I (3) (Formerly MATH 361). Homogeneous and non-homogeneous systems, matrix algebra, determinants, vector spaces and subspaces, bases, orthogonal bases, linear transformations, and rank. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all Mathematics, Physics, and Computer Science majors. Offered in fall, spring, and summer.
MATH 3620 Linear Algebra II (3) (Formerly MATH 362). A continuation of MATH 3610. It is strongly recommended that 3610 and 3620 be taken sequentially. Topics include a further treatment of linear transformations, rank, eigenvalues, eigenvectors, and the spectral theorem. Prerequisite: grade of C or better in MATH 3610. Required of all Mathematics majors. Offered in spring.
MATH 3640 Abstract Algebra (3) (Formerly MATH 364). An introduction to properties of groups, rings, integral domains, and fields. Prerequisites: grades of C or better in MATH 1920 and 3210, or permission of Department Head. Required of all Mathematics majors. Offered in spring.
MATH 3710 Teaching Mathematics in the Secondary School (3) (Formerly MATH 371). Lectures, discussions, and reports on materials and methods used in the instruction of mathematics at the middle school and high school level. Clinical and field-based experiences which call for active participation by students are part of the course requirements. Required of all students seeking certification in Mathematics. Prerequisite: official admission to the Teacher Education Program. Offered in spring.
MATH 3810 Geometry (3) (Formerly MATH 381). A brief review of Euclidean geometry with further topics, including the non-Euclidean and projective geometries. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Required of all teacher certification candidates in Mathematics. Offered in fall of odd numbered and summer of even-numbered years.
MATH 3900 Introduction to Numerical Analysis (3) (Formerly MATH 390). Errors, interpolation, approximations, numerical quadrature, solution of ordinary differential equations. Prerequisite: grade of C or better in MATH 1920 or permission of the Department Head. Offered on demand.
MATH 4310, 4320 Topology I, II (3, 3) (Formerly MATH 431, 432). Homeomorphisms, connectedness, compactness, metric spaces, normal spaces, Urysohn ’ s lemma, Tietze ’ s theorem, separation axioms, product topology, Hilbert space, quotient space, paracompactness, nets, and filters, with an introduction to homotopy theory. Prerequisites: grades of C or better in MATH 2110, and 3510, or permission of the Department Head. Offered on demand.
MATH 4410, 4420 Advanced Calculus I, II (3, 3) (Formerly MATH 441, 442). A variety of topics including functions of several variables; the algebra and topology of Euclidean n-space; differentials; extrema; the gradient; line, surface and volume integral; Stokes ’ theorem; inverse mapping theorem; and manifolds. Prerequisites: grades of C or better in MATH 2110, 3510, and 3610, or permission of the Department Head. Mathematics majors must take this sequence or MATH 4640-4650 or STAT 4210-4220. MATH 4410 is offered in fall and 4420 in spring.
MATH 4500 Senior Project (3) (Formerly MATH 450). A comprehensive inquiry into the nature of mathematics . Emphasis is on written presentation of the subject matter. Required of all prospective graduating seniors in Mathematics. Prerequisite: senior standing. Offered in fall.
MATH 4510, 4520 Real Analysis I, II (3, 3) (Formerly MATH 451, 452). Set theory, algebra, and topology of the real numbers, continuous functions, uniform convergence, measure and integration theory, Lebesque measure and integrals, convergence theorem, L-spaces, Banach spaces, differentiation, Radon-Nikodym theorem, Fubini theorem. Prerequisite: grade of C or better in MATH 4420 or permission of the Department Head. Offered on demand.
MATH 4530, 4540 Complex Analysis I, II (3, 3) (Formerly MATH 453, 454). Analytic functions, Cauchy ’ s integral theorem, Taylor and Laurent series, singularities, residue theory, analytic continuation, conformal mapping, Riemann surfaces, infinite products, and entire functions. Prerequisite: grade of C or better in MATH 442 or permission of the Department Head. MATH 4530 is offered in fall of odd-numbered years and 4540 is offered in spring of even-numbered years.
MATH 4560, 4570 Differential Equations I, II (3, 3) (Formerly MATH 456, 457). First- and second-order equations, general theory of linear nth-order differential equations, constant coefficient systems, variation of parameters, infinite series, singular solutions, asymptotic solutions, Green ’ s functions, stability, special functions, Laplace transform. Prerequisites: grades of C or better in MATH 3030 and 3620, or permission of the Department Head. MATH 4560 is offered in fall of even-numbered years and spring of odd-numbered years.
MATH 4640, 4650 Modern Algebra I, II (3, 3) (Formerly MATH 464, 465). Equivalence relations, mappings, groups, rings, fields, polynomial rings, modules, vector spaces, Galois theory. Prerequisites: grades of C or better in MATH 3210, 3620, and 3640, or permission of the Department Head. Mathematics majors must take this sequence or MATH 4410-4420 or STAT 4210-4220. MATH 4640 is offered in the fall and 4650 in the spring.
MATH 4724 Student Teaching of Mathematics in the Secondary Schools (9) (Formerly MATH 472S). A semester-long experience of supervised practice teaching, appropriately divided between middle school and high school. Required of all students seeking certification in teaching mathematics. Prerequisite: successful completion of all certification courses except EDCI 4705, which is taken concurrently. Offered on demand.
MATH 4730, 4740 Logic I, II (3, 3) (Formerly MATH 473, 474). Introduction to mathematical logic. Logic I is a survey of fundamental material including the statement calculus and the predicate calculus. Logic II is an introduction to Fuzzy Logic and Gödel ’ s Incompleteness Theorem. Prerequisite: grade of C or better in MATH 2110 or permission of the Department Head. Offered on demand.
MATH 4750 History of Mathematics (3) (Formerly MATH 475). The origin and development of mathematical ideas, beginning with geometry and algebra and continuing through selected topics in modern mathematics. Prerequisite: grade of C or better in MATH 2110 or permission of the Department Head. Offered in fall or even numbered and summer of odd-numbered years.
MATH 4900 Special Topics (3) (Formerly MATH 490). Special topics in mathematics to be offered with permission of the undergraduate mathematics curriculum committee in response to the preference and needs of the students. Repeatable to six hours. Prerequisite: permission of the Department Head. Offered in fall, spring, and summer.
Statistics (STAT)
STAT 1510, 1520 Introduction to Probability and Statistics I, II (3, 3). An overview of what statistics is and what statisticians do. Topics include basic concepts of probability, random variables and probability distributions, basic concepts of inference, linear regression and correlation, analysis of variance, and analysis of enumerative data. Prerequisite: permission of the Department Head. STAT 1510 is offered in fall and 1520 on demand.
STAT 3110, 3120 Probability and Statistics I, II (3, 3) (Formerly STAT 311, 312). Probability as a tool for inference: the axioms of probability, random variables and their probability distributions, multivariate probability distributions, functions of random variables, hypothesis testing, linear models and estimation by least squares, the general linear model, analysis of categorical data, and non-parametric statistics. Prerequisite: MATH 1920 or permission of the Department Head. STAT 3110 is required of all Computer Science majors. STAT 3110 is offered every semester; 3120 is offered only in the spring.
STAT 3700 Introduction to Statistical Computing and Data Management (3) (Formerly STAT 370). Components of digital computers, characteristics of magnetic storage devices, use of JCL and utility programs, concepts and techniques of research data management. Prerequisites: MATH 1920 and CS 222, or permission of the Department Head. Offered on demand.
STAT 4210 Statistical Methods I (3) (Formerly STAT 421). Approaches to the problems of description and goodness of fit; univariate location and scale; elvariate independence and correlation; comparison of independent or matched samples, involving categorical, discrete, or continuous data; non-parametric tests. Prerequisite: STAT 3120 or permission of the Department Head. All Mathematics majors must take the STAT 4210-4220 sequence or MATH 4410-4420 or MATH 4640-4650. Offered in fall.
STAT 4220 Statistical Methods II (3) (Formerly STAT 422). A continuation of STAT 4210. Topics include simple and multiple regression, analysis of variance and covariance, elements of experimental design and analysis, random effects models, simultaneous inference and the general linear model in matrix terms. Prerequisite: STAT 4210 or permission of the Department Head. Offered in spring.
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