Department Chairperson:Rohan Attele Faculty:Victor K. Akatsa, Kapila Rohan Attele, Jan-Jo Chen, Johng-Chern Chern, Raymond H. Y. Chu, John F. Erickson, Dawit Getachew, Lun-Pin Ho, Daniel J. Hrozencik, Lixing (Adam) Jia, Paul M. Musial, Sharon O’Donnell, Howard A. Silver (Emeritus), Richard J. Solakiewicz, Marjorie M. Stinespring (Emeritus), Luis Vidal-Ascon, Guang-Nay Wang, Jesse Y. Wang, Asmamaw Yimer, George I. Zazi The Department of Mathematics and Computer Science offers a Bachelor of Science degree in Mathematics with two options: (a) Mathematics (b) Secondary Teaching. Within the Mathematics option, a student may take an actuarial science concentration. The built-in flexibility of the Mathematics option will prepare students for careers in banks, insurance, industry, government, or to pursue advanced degrees in mathematics. Completion of the Secondary Teaching option in Mathematics qualifies students for an Initial Type 09 Illinois High School Certificate with a high school endorsement in mathematics for grades 9–12, and a middle grade endorsement in mathematics for grades 6–8. Certification requires the successful completion of the Illinois Certification Tests of Basic Skills, Mathematics, and Assessment of Professional Teaching (Secondary 6–12). The secondary teaching program is accredited by the National Council of Teachers of Mathematics (NCTM), and meets Illinois State Board of Education (ISBE) standards in mathematics education. The department offers a minor sequence in mathematics. It will provide students majoring in other disciplines access to more potent professional tools, and help them to gain a deeper understanding of their own fields. All entering freshmen and transfer students are required to take the university placement examination in mathematics. These students may not register for any mathematics or computer science course until they have taken the examinations. These examinations are designed to place students into the appropriate mathematics course from Applied Intermediate Algebra to Calculus. Students may not use MATH 0880/088, 0900/090, 0950/095, 0980/098, 0990/099, 160 or 161 toward satisfying general education mathematics or university graduation requirements. Credit will not be given for any mathematics course which is a prerequisite for a course in which a grade of C or better has already been earned. Admission to the program is contingent upon completion of MATH 1210/163 or MATH 1250/171 with a grade of C or higher, cumulative grade point average of 2.0 or higher, and acceptance by the department. The department will not accept D grades in any required major courses or required supportive courses, either as transfer credit or completed at Chicago State University. Requirements include completion of 120 semester hours of work: 39 hours in general education; 44 hours in mathematics; 15 hours of supportive courses; 22 hours in electives selected with the departmental advisor’s approval; and passing the examination on the state and federal constitutions. By demonstrating proficiency, a student may be able to obtain credit for certain mathematics and computer science courses at the recommendation of the department. The 9 credit hours in Physical and Life Sciences must be selected from BIOL/CHEM/PHYS/PHSCI and include at least one laboratory course. Required Courses (44 credit hours) MATH 1900/180, 2200/201, 2300/230, 1410/261 or 1415, 1420/262, 2430/263, 2550/271, 4110/342, and 4940/392; one of the following - MATH 4210/327, 4230/308, or 4250/361; one of the following – MATH 4410/358 or 4450/356; one of the following in applied mathematics – MATH 3820/325, 4510/354, 4520/355, 4600/315, 4650/318, 4800/350, or 4840/326; two additional courses selected from the above or MATH 2800/283, 3210/329, 3800/313, 4710/345, 4900/370. Required Supportive Courses (15 credit hours) Physical and Life Sciences that must be selected from BIOL/CHEM/PHYS/PHSCI: three additional credit hours; CPTR 1100/141, nine additional credit hours selected from accounting, biology, botany, chemistry (1550/155 or above); computer science (above 1100/141), economics, mathematics (2810/251 only), physics, zoology. At least two courses must be from the same discipline. Elective Courses (22 credit hours) 22 credit hours of electives selected with the department advisor’s approval. Required Courses (44 credit hours) MATH 1900/180, 1410/261 or 1415, 1420/262, 2200/201, 2300/230, 2430/263, 2550/271, 3630/274, 3800/313, 4110/342, 4600/315, 4650/318, and 4940/392; one of the following: MATH 2800/283, 3820/325, 4230/308, 4840/326, 4800/350 or 4900/370. Required Supportive Courses (15 credit hours) Physical and Life Sciences that must be selected from BIOL/CHEM/PHYS/PHSCI: three additional credit hours; complete one of the following two sets of courses: CPTR 1100/141, ACCT 2110/110 and 2111/111, and FIN 2660/266; or CPTR 1100/141, ACCT 2110/110, FIN 2660/266 and 3680/368. ECON 1010/101 and 1020/102 are strongly recommended to fulfill the General Education Social Science requirement. Elective Courses (22 credit hours) 22 credit hours of electives selected with the department advisor’s approval. To be considered for recommendation for admission to the College of Education, students must have: - completed MATH 1420/262 and two 4000/300-level mathematics courses with a grade of C or higher;
- completed with a grade of C or higher, or be concurrently enrolled in MATH 2430/263 and MATH 4110/342;
- passed the Illinois State Basic Skills Examination, and a 2.5 GPA or higher in 1000-level and above mathematics courses.
Students must: - Pass the examination on the state and federal constitutions.
- Complete 120 credit hours in: General Education 39 credit hours, Area of Specialization 50 credit hours, Professional Education 27 credit hours, Elective Courses 4 credit hours.
General Education 39 credit hours: the 3 hours in mathematics is satisfied by the major. In addition, the nine credit hours in Physical and Life Sciences must include a two-course science laboratory sequence. Also, the nine hours in Social Sciences must be chosen from the following: HIST 1300/130 or 1310/131 or POL 1010/101; PSYC 1100/141 and 2040/204. Required Mathematics Courses (47 credit hours) MATH 1900/180, 1410/261 or 1415, 1420/262, 2200/201, 2300/230, 2430/263, 4010/347, 4020/348, 4250/361, 4110/342, 4450/356 or 4410/358, 4600/315, and 4710/345; at least six additional hours selected from MATH 2550/271, 2800/283, 3210/329, 3820/325, 4210/327, 4230/308, 4410/358, 4450/356, 4510/354, 4650/318, 4800/350, 4840/326, 4900/370 or 4940/392. Required Supportive Courses: (3 credit hours) MATH 0920/092 or pass state teacher certification subject matter test in mathematics; MATH 2810/251 or three additional hours in the Physical and Life Sciences (BIOL/CHEM/PHYS/PH SCI). Professional Education (27 credit hours) ELCF 1520/152 and 2000/200; PSYC 2020/206; S ED 4301/301 and 4303/303*; ELCF 5500/353*; READ 4100/306*; CAS 3630/363*, MATH 4000/363* and 4005/375*. Course must be passed with at least a grade of C. * Restricted to students admitted to the College of Education. Sample Curriculum Pattern (Mathematics Option, Mathematics Concentration) **First Semester**
| ** **
| **Second Semester**
| ** **
| MATH 1410 or 1415* | 4 | MATH 1420 | 4 | | | MATH 1900 | 1 | ENG 1270 | 3 | ENG 1280 | 3 | Social Science** | 3 | Language | 3 | Language | 3 | Natural Science | 3 | Natural Science*** | 3 | MATH 2200 | 3 | | 16 | | 17 |
**Third Semester**
| ** **
| **Fourth Semester**
| ** **
| MATH 2430 | 4 | MATH 2550 | 4 | MATH 2300 | 3 | MATH 4210 | 3 | Social Science | 3 | Elective | 3 | Humanities | 3 | MATH 2810 | 3 | Natural Science | 3 | CPTR 1100 | 3 | | 16 | | 16 |
**Fifth Semester**
| ** **
| **Sixth Semester**
| ** **
| MATH 4250 | 3 | MATH 4410 | 3 | MATH 4110 | 3 | Math Elective | 3 | Elective | 3 | Social Science | 3 | Humanities | 3 | Fine Arts | 3 | Supportive Elective | 3 | Supportive Elective | 3 | | 15 | | 15 |
**Seventh Semester**
| ** **
| **Eighth Semester**
| ** **
| Applied Math | 3 | MATH 4940 | 3 | MATH 4450 | 3 | Math Elective | 3 | Supportive Elective | 3 | Elective | 4 | Elective | 3 | Elective | 3 | | 12 | | 13 |
* The first mathematics course is determined by the placement examination. ** Any one of HIST 1300/130, 1310/131, or POL 1010/101 or 2020/202 will satisfy the constitution examination requirement. *** Students must have at least one course in physical science and at least one course in biology including at least one laboratory course. Sample Curriculum Pattern (Mathematics Secondary Teaching Option) **First Semester**
| ** **
| **Second Semester**
| ** **
| MATH 1410 or 1415 | 4 | MATH 1420 | 4 | ENG 1270/127 | 3 | ENG 1280 | 3 | Language | 3 | PSYC 1100 | 3 | MATH 2200 | 3 | Language | 3 | Social Science | 3 | PSYC 2040 | 3 | Math 1900 | 1 | ELCF 152 | 2 | | 17 | | 18 |
**Third Semester**
| ** **
| **Fourth Semester**
| ** **
| MATH 2430 | 4 | MATH 4250 | 3 | MATH 2300 | 3 | Math Elective | 3 | CMAT 1130 | 3 | ELCF 2000 | 3 | PSYC 2020 | 3 | Elective | 4 | Natural Science** | 3 | Natural Science** | 3 | | 16 | | 16 |
**Fifth Semester**
| ** **
| **Sixth Semester**
| ** **
| MATH 4600 | 4 | MATH 4710 | 3 | MATH 4110 | 3 | MATH 4010 | 3 | Humanities | 3 | MATH 4450 or 4410 | 3 | S ED 4301/301 | 3 | Fine Arts | 3 | Nat. Science 3 | | MATH 0920 | 1 | | | Supp. Elective | 3 | | 15 | | 16 |
**Seventh Semester**
| ** **
| **Eighth Semester**
| ** **
| MATH 4040 | 3 | MATH 4005 | 6 | Math Elective | 3 | S ED 4303 | 2 | ELCF 5500 | 2 | READ 4100 | 2 | MATH 4000 | 3 | CAS 2630 | 1 | | 11 | | 11 |
* The first mathematics course is determined by the placement examination. ** Students must have at least one course in physical science and at least one course in biology including a two-course laboratory sequence. *** Restricted to students admitted to the College of Education. The requirements for minors must be completed prior to graduation in order for the minor to appear on the transcript. For more information about minors, see the Department Advisor. Required Courses (15 credit hours) MATH 1410/261 or 1415, 1420/262, 2430/263, 2200/201. Elective Courses (9–11 credit hours.) Three additional mathematics courses from Math 2550/271, 2800/283, or those numbered 4230/308 or above. Students enrolling in mathematics classes must receive at least a grade of C in all prerequisite mathematics and computer science courses. 0880/088 TUTORIAL ALGEBRA (1) Prerequisite: Mathematics Placement Examination. Elementary geometry, signed numbers, percents, ratios, linear equations, exponents, operations on polynomials, and applications. Credit does not count toward graduation; graphing calculator is required. 0910/091 ILLINOIS TEACHER CERTIFICATION REVIEW OF BASIC SKILLS IN MATHEMATICS (1) Prerequisites: Completion of mathematics requirements in the student’s major, or consent of department. Review of mathematics concepts, skills, and problem solving to prepare the basic skills mathematics portion of the state teacher certification examination. May be repeated. Credit may not be used toward graduation. 0920/092 ILLINOIS MATHEMATICS TEACHER CERTIFICATION REVIEW (1) Co-requisite: MATH 2430/263 and consent of the department. Review of mathematics concepts and problem solving to prepare for state teacher certification examination. May be repeated. Credit does not count toward graduation. 0990/099 APPLIED INTERMEDIATE ALGEBRA (4, 8) Prerequisites: Mathematics Placement Examination Level 1 : Elementary geometry, signed numbers; applications of percents, ratios, and linear equations; equations of lines, exponents, operations on polynomials.Level 2: More in-depth study of Level 1 topics; systems of equations, graphing, rational expressions, quadratics, and radicals. Credit does not count toward graduation, graphing calculator is required. Additional Course Fee. 1010/140 CONCEPTS OF MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS I /4 (3) Prerequisite: MATH 0990/099 or by placement examination; READ 1500/150; ENG 1280/128 or concurrent enrollment. Patterns and problem solving, numeration systems, functions, algorithms for whole numbers, integer, decimal, and rational number operations (addition, subtraction, multiplication, division), divisibility tests, GCD, LCM, ratio and proportion, percents, statistical graphs, measures of central tendency and variation. IAI: M1 903 1020/141 CONCEPTS OF MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS II /4 (3) Prerequisite: MATH 1010/140. Points, lines, planes, curves, angles, three-dimensional figures, congruence, similarity, construction, English system, metric system, perimeter, area, volume, Pythagorean theorem, probability. IAI: M1 903 1200/162 COLLEGE ALGEBRA /4 (3) Prerequisite: MATH 0990/099 or by placement examination. Equations and inequalities, rectangular coordinates, lines, functions and their graphs, polynomials and rational functions, exponential and logarithmic functions, and systems of equations. Graphing calculator required. 1210/163 COLLEGE ALGEBRA AND TRIGONOMETRY /4 (3) Prerequisite: MATH 1200/162 or by placement examination, or Hon 1300/130 & 1310/131. Exponential and logarithmic functions, systems of equations, trigonometric functions, solution of triangles, mathematical induction, sequences, polar coordinates, and conics. Graphing calculator required. 1250/171 PRECALCULUS MATHEMATICS /6 (5) Prerequisite: MATH 0990/099 or consent of the department. Sets; real numbers; theory and application of functions and inverse functions; trigonometric functions; complex numbers; exponentials and logarithms; matrices and determinants; vectors. Graphing calculator required. 1400/209 BASIC CALCULUS (3) Prerequisite: MATH 1200/162 or 1250/171 or by placement examination, or HON 1300/130 & 1310/131. Functions and limits; the derivative and its applications; the integral and its applications. Graphing calculator required. IAI: M1 900. 1410/261 CALCULUS I (4) Prerequisite: MATH 1210/163 or MATH 1250/171 or by placement examination. Limits and continuity, derivatives of algebraic and trigonometric functions, chain rule, applications (such as extreme problems, related rates, graphing), anti-derivatives, definite integral, applications (such as area, volume, work, force). Graphing calculator required. IAI: M1 900, EGR 901, MTH 901. 1415 CALCULUS FOR LIFE SCIENCES–1 (4) Prerequisites: MATH 1210/163 or MATH 1250/171 or by placement examination Sequences, difference equations, discrete time models, limits, continuity, differentiation and anti-differentiation of algebraic, trigonometric, and transcendental functions, chain rule, applied problems on maxima and minima, equilibria and stability, basic differential equations, and the fundamental theorem of calculus. CAS, modeling, and imaging programs. Strong emphasis on biological models using real biological data. Course fee. 1420/262 CALCULUS II (4) Prerequisite: MATH 1410/261 or 1415, or by placement examination; For math majors only: MATH 1900/180 (or concurrent enrollment). Calculus of the exponential, logarithmic, and trigonometric functions, techniques of integration, L’Hospital’s rule, improper integrals, infinite series, and polar coordinates. Graphing calculator required. IAI: M1 900, EGR 902, MTH 902 1500/214 INTRODUCTION TO FINITE MATHEMATICS (3) Prerequisite: MATH 1200/162 or 1250/171 or by placement examination, or HON 1300/130 & 1310/131. Probability; model building; linear programming; matrices. Emphasis on applications in business and social science. Graphing calculator required. IAI: M1 906 1600/210 BASIC PROBABILITY AND STATISTICS (3) Prerequisite: MATH 1200/162 or 1250/171 or by placement examination, or HON 1300/130 & 1310/131. Sample spaces; set functions; probability; random variables; probability distributions; mean, median, and standard deviations; sampling; hypothesis testing; tests concerning means. Graphing calculator required. IAI: M1 902 1700/121 INTRODUCTION TO MATHEMATICAL THOUGHT (3) Prerequisite: MATH 0990/099 or by placement examination. Mathematical reasoning and solving real world problems. In depth study of three or four of the following topics: geometry, counting techniques and probability, graph theory, logic/set theory, mathematical modeling, game theory, and linear programming. Graphing calculator required. IAI: M1 904 1800/123 QUANTITATIVE LITERACY (3) Prerequisite: MATH 0990/099 or by placement examination; READ 1500/150. Develops conceptual understanding for problem solving and decision making; uses analytic skills including statistical measures, graphs of functions, estimation, and selection and use of appropriate approaches for formulating and solving real world problems. Graphing calculator required. May be taken before or after MATH 1700/121. IAI: M1 901 1900/180 INTRODUCTION TO MATHEMATICS PROFESSIONS (1) Prerequisite: MATH 1210/163 A survey of career opportunities for mathematics professionals in industry, government, and education. Overview of the skills, training, strategies, and education required for the various occupations and mathematics curricula. Introduction to the resources available to aid the mathematics major. May not be used to fulfill general education requirements. 2200/201 LINEAR ALGEBRA (3) Prerequisite: MATH 1210/163 or 1250/171 or by placement examination. Matrices and vectors; transformations and matrices; matrix and vector products; determinants; applications. Graphing calculator required. 2300/230 INTRODUCTION TO HIGHER MATHEMATICS (3) Prerequisites: MATH 1420/262 Techniques of proof through the study of concepts used in higher mathematics courses. Set theory, logic, epsilon-delta proofs, proof by contradiction, equivalence relations, functions, cardinality, mathematical induction. 2430/263 CALCULUS III (4) Prerequisite: MATH 1420/262; MATH 2200/201 or concurrent enrollment or PHYS 2110/211 or concurrent enrollment. Parametric equations, vectors and vector functions, calculus of functions of several variables, gradients, multiple integrals, line integrals, Green’s theorem. Graphing calculator required. IAI: M1 900, EGR 903, MATH 903. 2710/271 DIFFERENTIAL EQUATIONS (4) Prerequisite: MATH 2430/263. First order differential equations with applications; numerical methods, linear differential equations with applications, power series, and Laplace transforms. IAI: EGR 904 MTH 912 2800/283 DISCRETE MATHEMATICS (3) Prerequisite: CPTR 1100/141 and MATH 1200/162 or 1250/171, or Hon 1300/130 & 1310/131. Relations, functions, permutations, combinations, sets, logic, Boolean algebra, graph theory. Credit is given for only one of the following: MATH 300, MATH 303, or MATH 2800/283. IAI: M1 905, CS 915. 2810/251 INTRODUCTION TO RESEARCH IN BIO-MATHEMATIC/4 (3) Prerequisites: MATH 2200/201; BIOL 1070/107 and 1080/108 Introduction to mathematical software in biological modeling, difference equations in Microsoft Excel, matrix methods, eigen values, linearization and stability, equilibria. Further topics may include: phylogenetics, population dynamics, and ecology. Data will be collected in the field. Term paper required. Credit is not given for both MATH 2810/251 and BIOL 2810/251. 3210/329 MATHEMATICAL LOGIC (3) Prerequisite: MATH 1410/261 or 1415 and MATH 2300/230 or consent of the department. A formal study of the propositional calculus and the predicate calculus, including formal semantics and taxiomatizations. Completeness theorems for both systems will be proven. 3630/274 REVIEW FOR ACTUARIAL EXAMINATION 100 /3 (2) Prerequisite: Grade of C or better in MATH 2200/201, 1410/261, 1420/262, 2430/263, and 2550/271. Specifically designed for preparation for Actuarial Examination 100. Emphasis on problem solving. Practice examinations. 3800/313 THEORY OF INTEREST (3) Prerequisite: MATH 1420/262 Measure of interest, accumulated and present value factors, annuities certain, yield rates, amortization schedules and sinking funds, bonds and related securities. Spread sheets used. 3820/325 LINEAR PROGRAMMING (3) Prerequisite: MATH 2200/201 or 1500/214. Linear equations, problem formulation, simplex method, duality theory, post-optimal analysis, transportation problem, game theory. 4000/363 METHODS OF TEACHING MATHEMATICS IN SECONDARY SCHOOLS (GRADES 6 - 12) /FIELD (3) Prerequisites : MATH 2200/201, 2430/263, 4100/342; admission to College of Education; MATH 0920/092, CAS 2630/363, MATH 4010/347 or CPTR 1100/141, ELCF 5500/353 and READ 4100/306 (or concurrent enrollment in MATH 0920/092, CAS 2630/363, MATH 4010/347 or CPTR 1100/141, ELCF 5500/353 and READ 4100/306; consent of department. Methods of teaching mathematics in high school grades 9-12 and middle school grades 6-8. Thirty hours of tutoring middle grade and high school grade students. May not be used toward mathematics requirements for a major or minor in mathematics. 4005/375 STUDENT TEACHING AND SEMINAR-SECONDARY LEVEL/FIELD (6) Prerequisite: Admission to the College of Education; Completion of all coursework required in the program with a grade of C or higher; a 2.5 grade point average in all coursework; a 2.5 grade point average in the area of specialization; consent of the department; and a passing score on the subject matter/content area certification test within the last 5 years. Off-campus placement in secondary schools in two or more grade levels. University and cooperating school supervision. Five full days including seminar for 16 weeks. No other courses may be taken during the semester of student teaching. May not be used to satisfy mathematics requirements for a major or minor in mathematics. 4010 /347 TECHNOLOGY IN THE HIGH SCHOOL MATHEMATICS CLASSROOM (3) Prerequisite: One 3000/300-level or higher mathematics course. Appropriate technological tools, including spreadsheets, geometry software, computer algebra systems, statistical packages, graphing calculators, data-collection devices, presentation software. Additional course fee. 4020/348 MATHEMATICS FOR HIGH SCHOOL TEACHERS (3) Prerequisites: MATH 2430/263, MATH 4110/342, one additional 3000/300-level or higher mathematics course (or concurrent enrollment). Advanced perspective in mathematics for pre- and in-service high school teachers; topics include geometry, functions, numbering systems, proofs. 4040/304 NUMBER THEORY FOR MIDDLE SCHOOL TEACHERS (3) Prerequisite: MATH 1020/141 or MATH 1200/162 or HON 1300/130 &1310/131; AND A 2000-LEVEL MATHEMATICS COURSE. Prime numbers. Euclidean algorithm. Greatest common divisors and least common multiples. Modular arithmetic. Diophantine equations. Integration of the content in elementary and middle school. May not be used for graduation credit in Mathematics or Mathematics Secondary Education options. 4050/305 GEOMETRY FOR MIDDLE SCHOOL TEACHERS (3) Prerequisite: MATH 1020/141 or MATH 1200/162 or equivalent or HON 1300/130 & 1310/131; and a 2000-level mathematics course. Incidence relation, angles, congruence, measurement, compass-and-straightedge constructions, circles, similarity, right-triangle trigonometry, area, volume, coordinate geometry in two and three dimensions, polygons, arcs and arc length. Integration of content in the elementary and middle school. May not be used for graduation credit in Mathematics or Mathematics Secondary Education options. 4060/306 MODERN ALGEBRA FOR MIDDLE SCHOOL TEACHERS (3) Prerequisite: MATH 1020/141 or MATH 1200/162, or HON 1300/130 & 1310/131 or equivalent; and a 2000-level mathematics course. An introduction to modern algebra. Topics chosen from: groups, rings, fields and their applications. May not be used for graduation credit in Mathematics or Mathematics Secondary Education options. 4070/307 HISTORY OF MATHEMATICS FOR MIDDLE SCHOOL TEACHERS (3) Prerequisites: MATH 1400/209 and MATH 4050/305 or equivalent. The historical basis of numeration, operations, geometry, algebra, trigonometry and calculus. The cultural aspect of mathematics and its contributions to knowledge and learning. Integration of content in the elementary and middle school. May not be used for graduation credit in Mathematics or Mathematics Secondary Education options. 4110/342 GEOMETRY (3) Prerequisite: MATH 1410/261 or 1415 and 2300/230; and one unit of high school plane geometry (regular or honors) with a grade of C or higher, or MATH 4050/305, or equivalent. Incidence geometry, distances, measure, congruences, inequalities, parallel postulate, perpendicular lines and places, similar triangles, polygons, circles and spheres, construction with ruler and compass. Writing emphasis course. 4210/327 ELEMENTARY NUMBER THEORY (3) Prerequisite: MATH 1410/261 or 1415, 2200/201, and 2300/230. Properties of integers, divisibility, greatest common divisors, primes, congruences, Diophantine equations, arithmetic functions, quadratic residues. 4230/308 MATRICES AND LINEAR TRANSFORMATIONS (3) Prerequisite: MATH 1420/262 and 2200/201. Vector spaces, bases, dimensionality, linear transformations, determinants, matrices, matrix inversion, rank, equivalence. 4250/361 INTRODUCTION TO MODERN ALGEBRA I (3) Prerequisite: MATH 1420/262 and 2200/201 and 2300/230. Basic properties of groups, order, cyclic groups and their structure theorems. Normal subgroups, cosets and Lagrange’s theorem, group homomorphisms, factor groups, direct products, and the isomorphism theorems; permutation groups. Basic properties of rings, integral domains, fields, ideals, ring homomorphisms; polynomial and power series rings. 4260 INTRODUCTION TO MODERN ALGEBRA II (3) Prerequisites: Math 4250 Group action, cojugacy classes, class equation, Cauchy’s theorem and p-groups, applications of Sylow theorems. Principal ideal domains, Euclidean domains, unique factorization domains. Maximal and prime ideals, rings of matrices, polynomial rings of several variables. At instructor’s discretion more topics from finite fields, and/or coding theory, and topics for undergraduate research in algebra. 4410/358 INTRODUCTION TO REAL VARIABLES (3) Prerequisite: MATH 2300/230 and 2430/263. Real numbers, real functions, limits, continuity, uniform continuity, differentiability, mean value theorems, theory of the Riemann integral. 4450/356 INTRODUCTION TO COMPLEX VARIABLES (3) Prerequisite: MATH 2300/230 and 2430/ 263. Complex numbers and complex space, differentiation and integration of elementary functions, infinite series, Taylor and Laurent expansions, Cauchy’s theorems and applications. 4510/354 NUMERICAL ANALYSIS I (3) Prerequisite: MATH 2430/263. Solution of linear systems by direct and iterative methods, matrix inversion, evaluation of determinants, characteristic values and vectors of matrices, application of boundary value problems in ordinary differential equations, numerical solution of partial differential equations. 4520/355 NUMERICAL ANALYSIS II (3) Prerequisite: MATH 4510/354. Continuation of mathematics 4510/354. 4600/315 INTRODUCTION TO STATISTICS LECTURE AND LABORATORY /5 (4) Prerequisite: MATH 1420/262. Descriptive statistics, discrete and continuous random variables, expectation, distribution functions, central limit theorem, point estimation, confidence intervals, and hypothesis testing. SAS Laboratory. Additional course fee. 4650/318 PROBABILITY AND MATHEMATICAL STATISTICS (3) Prerequisite: MATH 2430/263 and 4600/315. Moment generating functions, transformations of random variables, Bayes Theorem, sufficiency, likelihood estimators, Chi-square tests, regressions and contingency tables. SAS used. 4710/345 HISTORY OF MATHEMATICS (3) Prerequisite: MATH 1420/262 and 4110/342, or equivalent. Chronological survey of the growth and contributions of mathematics to knowledge and learning. 4800/350 MATHEMATICAL METHODS OF PHYSICS (3) Prerequisites: MATH 2550/271 and at least one calculus based physics course. Coordinate systems, vector analysis, special functions, Fourier analysis, Green’s functions, boundary value problems, matrices, and tensors. Credit not given for both PHYS 3450/345 and MATH 4800/350 4840/326 INTRODUCTION TO OPERATIONS RESEARCH (3) Prerequisite: MATH 2200/201 or 1500/214; and MATH 1400/209 or 1410/261 or 1415. Linear programming, game theory, dynamic programming, graph theory and Markov chains. Emphasis on applications in business, industry, and behavioral sciences. 4900/370 SPECIAL TOPICS IN MATHEMATICS (1–3) Prerequisite: To be determined by instructor and consent of the department. Topics of current mathematical interest. May be repeated for credit if different topics are presented. 4920/381 MATHEMATICS INTERNSHIP (3–6) Prerequisite: Grade of C or higher in three 3000-level mathematics courses earned 80 semester hours toward a baccalaureate degree, and a major in mathematics; or consent of the department. A student project or activity in a mathematics environment outside the department where the techniques of mathematics are applied in an essential way. Activity to be performed must be approved in advance by the department. A written final report is required. Course may be repeated for a total of up to nine semester hours. 4940/392 MATHEMATICS SEMINAR (3) Prerequisite: MATH 2430/263 and nine credit hours of mathematics courses numbered 4230/308 or above. Investigation of mathematical models in fields such as natural sciences, social sciences, business and engineering. Scientific calculators, graphing calculators, and current computer software will be used. Specific topics will vary. Writing emphasis course. |