Department of Mathematics Main Departmental Office General Academic Building, 418 P.O. Box 5116 Denton, TX 76203-0116 (817) 565-2155 Fax: (817) 565-4805 John E. Allen, Chair Faculty Professors Appling, Bilyeu, Castro, Kallman, Kung, Lewis, Mauldin, Neuberger, Vaughan, Vest. Associate Professors Allen, Bator, Brand, Hagan, Hill, Jackson, Urbanski, Warchall. Assistant Professors Anghel, Arvola, Brozovic, DeLatte, Hoemeke, Iaia, Maher, Michler, Monticino, Santos, Underwood, Zamboni. Introduction The department offers programs of study leading to the BA, BS, MA, MS and PhD degrees with a major in mathematics. Its faculty is dedicated to excellence in scholarship and teaching. The faculty supports a strong program of instruction and research, having as its core a solid foundation of mathematical theory that furnishes the necessary environment for addressing and solving crucial problems related to maintaining, improving and protecting the world in which we live. It also seeks to promulgate mathematics as a discipline in its own right, pursuing self-generated goals, and seeks to exhibit it as one model of ideal human knowledge that enables its practitioners and those who diligently study it to be adaptable and effective forces in the workplace. Students who earn degrees in mathematics readily obtain jobs with high-technology companies and in business, industry, government and teaching. Salaries and working conditions match those of engineers and scientists. Students who plan to major in mathematics, physics, chemistry, biology or computer sciences should have had four years of mathematics in high school, including pre-calculus. Students who are required to take mathematics as part of their degree program in college should have had at least two years of algebra and one year of geometry in high school. Required Placement and Testing All students enrolling for their first UNT mathematics course are required to take a placement examination and obtain a course approval form from the mathematics department. Consult the Schedule of Classes for details. Students who are required to take mathematics must enroll for the appropriate mathematics class during their first year at UNT. Programs of Study The department offers undergraduate and graduate programs in the following areas: -Bachelor of Arts, -Master of Arts, -Master of Science, and -Doctor of Philosophy, all with a major in mathematics; and -Bachelor of Science in Mathematics. Bachelor of Arts Degree Requirements A minimum of 128 hours is required, of which 42 must be advanced, and fulfillment of degree requirements for the Bachelor of Arts degree as specified in the College of Arts and Sciences section of this catalog. Major in Mathematics Following is one suggested arrangement of courses distributed over four years. BA with a Major in Mathematics FRESHMAN YEAR FALL HOURS MATH 1710, Calculus I{1} 4 LANG 2040, Foreign Language (intermediate){2} 3 CSCI 1110, Program Development 3 ENGL 1310, College Writing I 3 Laboratory Science{3} 4 Total 17 SPRING HOURS MATH 1720, Calculus II 3 LANG 2050, Foreign Language (intermediate){2} 3 ECON 1110, Macroeconomics 3 ENGL 1320, College Writing II{4} 3 Laboratory Science{3} 4 Total 16 SOPHOMORE YEAR FALL HOURS MATH 2510, Real Analysis I 3 MATH 2730, Multivariable Calculus 3 ENGL 2210, World Literature 3 HIST 2610, United States History to 1865{5} 3 Laboratory Science{3} 4 Total 16 SPRING HOURS MATH 2520, Real Analysis II 3 MATH 2700, Linear Algebra and Vector Geometry 3 ENGL 2220, World Literature 3 HIST 2620, United States History Since 1865{5} 3 Laboratory Science{3} 4 Total 16 JUNIOR YEAR FALL HOURS MATH 3510, Introduction to Abstract Algebra I{6} 3 PSCI 1040, American Government 3 Visual and Performing Arts{7}* 3 PHED 1000, Scientific Principles and Practices of Health-Related Fitness, or DANC 1100, Stress Reduction Through Movement 2-3 Minor Concentration{8} 3 Elective 3 Total 17-18 SPRING HOURS MATH (above 3150) 6 PSCI 1050, American Government 3 Understanding of Ideas and Values{9}* 3 Minor Concentration 3 Total 15 SENIOR YEAR FALL HOURS MATH 4610, Probability 3 PHIL{10} 3 Minor Concentration 6 Elective 4 Total 16 SPRING HOURS MATH (above 3150) 3 Minor Concentration 6 Elective 3 Understanding of Ideas and Values{9}* 3 Total 15 Total Minimum Hours Required: 128 Note: Some courses may require prerequisites not listed in the above plan. {1} Students should consult the Department of Mathematics for proper placement into the appropriate level before beginning their mathematics program. {2} Contact the Department of Foreign Languages and Literatures for proper placement into the appropriate level. Students must demonstrate proficiency by exam or complete the required prerequisites (LANG 1010- 1020) before enrolling in LANG 2040 or 2050. {3} Mathematics majors must complete two courses of natural/life science in the same discipline, either BIOL 1610-1630 and 1620-1640, or GEOL 1610 and 1620. They also must complete two courses of physical science in the same discipline, either CHEM 1410-1430 and 1420-1440, or PHYS 1710-1730 and 2220-2240. {4} Students who plan to take ENGL 2700 in place of ENGL 1320 should follow this sequence: ENGL 1310, 2210, 2220, 2700. {5} Advanced American/Texas History courses may be substituted to help meet the 42 advanced hours degree requirement. {6} 2.0 GPA required in all mathematics courses above MATH 3150. {7} See "University Core Curriculum Requirements" in the Academics section of this catalog for a list of approved Visual and Performing Arts courses. Note: ART 1300, 2350 may not be used to satisfy both the Visual and Performing Arts requirement and the Understanding of Ideas and Values, Group II requirement. {8} Hours in the minor may vary. For hours in a specific minor contact your major departmental adviser. {9} Understanding of Ideas and Values: One course per group from any two of Groups I, II, III. See "University Core Curriculum Requirements" in the Academics section of this catalog for a list of approved courses. {10} PHIL 2050, 2310, or 2330 also will satisfy 3 hours of the Understanding of Ideas and Values, Group I requirement. See "Arts and Sciences Core Curriculum" in the College of Arts and Sciences section of this catalog for a list of approved courses. * Taking courses in the minor and core at the advanced level will aid the student in reaching the 42 advanced hours necessary for graduation. Additional advanced elective courses may be required if this course is not chosen at the advanced level. The student is responsible for reaching 42 total advanced hours. See your faculty adviser each semester for help in program decisions and preparation for enrollment. Supplemental Information for BA with a Major in Mathematics 1. Required courses: MATH 1710, 1720, 2510, 2520, 2700, 2730, 3510 and 4610, plus 9 hours numbered above 3150. Required laboratory science must include either PHYS 1710, 1730, 2220, 2240 or CHEM 1410, 1420, 1430, 1440, and either BIOL 1610/1630-1620/1640 or GEOL 1610-1620. 2. It is recommended that the required foreign language be German, French, Spanish or Russian. Students who wish to take some other language should consult the chair of the mathematics department. Students should consult the College of Arts and Sciences section and "University Core Curriculum Requirements" in the Academics section of the catalog for general requirements for the Bachelor of Arts degree and make a degree plan in consultation with faculty advisers. Bachelor of Science in Mathematics Degree Requirements Candidates for the Bachelor of Science in Mathematics must meet the following requirements. 1. Hours Required for the Degree: Completion of a minimum of 130 total semester hours; 42 must be advanced. 2. General University Requirements: See "General Degree Requirements" in the Academics section of this catalog. 3. College of Arts and Sciences Core Curriculum: Minimum 61 hours (includes requirements of University Core Curriculum). See "Arts and Sciences Core Curriculum" in the College of Arts and Sciences section of this catalog for specific core requirements and list of approved courses. 4. Major Requirements: 43 hours of which 24 must be advanced, including MATH 1710, 1720, 2510, 2520, 2700, 2730, 3410, 3510, 4500, 4520, and 4610, plus one course from each of the three groups below: -Group A: MATH 3740, 4100, 4650 -Group B: MATH 3400, 3520, 4200 -Group C: MATH 3350, 3420, 4450 5. Minor Requirements: A minor in one of the following areas of study: -Biology: BIOL 1610-1630, 1620-1640, 3050, 3450, 3510 and 6 additional hours of advanced biology other than 4700; CHEM 1410- or 1413-1430, 1420- or 1423-1440 and 3600, or both 2370 and 2380. -Chemistry: CHEM 1410- or 1413-1430, 1420- or 1423-1440, 2370, 2380, 3450, 3510, and 3520; PHYS 1710-1730 and 2220-2240. -Computer Science: 1110, 1120, 2010, plus 15 advanced hours. -Physics: PHYS 1710-1730, 2220-2240, 3010-3030, 3210, and 9 additional hours of advanced physics. 6. Electives: See four-year plan. 7. Other Course Requirements: The laboratory science requirement must be met with the following: PHYS 1710-1730, 2220-2240 or CHEM 1410-1430, 1420-1440, and either BIOL 1610-1630, 1620-1640 or GEOL 1610, 1620. 8. Other Requirements: Bachelor's degree candidates in mathematics must present at least a 2.0 grade point average on all mathematics courses above 3150. See the Chair of the Department of Mathematics or the undergraduate adviser for a degree plan during the first year of study at UNT. In order to teach mathematics at the secondary level, students are required to obtain a bachelors degree in mathematics. In addition, 21 hours in the College of Education (including student teaching) are required. Students taking mathematics courses at the 3000-level or above are expected to be competent in computer programming, using languages such as BASIC, C, Fortran, or PASCAL. This competency can be obtained through completion of CSCI 1110. It is recommended that the required foreign language be German, French, Russian, or Spanish. Students wishing to take some other language must consult the Chair of the Department of Mathematics. DRED (Traffic Safety) courses may not be used to satisfy any portion of a degree in the College of Arts and Sciences. BS in Mathematics Following is one suggested arrangement of courses distributed over four years. BS in Mathematics FRESHMAN YEAR FALL HOURS MATH 1710, Calculus I{1} 4 LANG 2040, Foreign Language (intermediate){2} 3 CSCI 1110, Program Development 3 ENGL 1310, College Writing I 3 Laboratory Science{3} 4 Total 17 SPRING HOURS MATH 1720, Calculus II 3 LANG 2050, Foreign Language (intermediate){2} 3 ECON 1110, Macroeconomics 3 ENGL 1320, College Writing II{4} 3 Laboratory Science{3} 4 Total 16 SOPHOMORE YEAR FALL HOURS MATH 2510, Real Analysis I 3 MATH 2730, Multivariable Calculus 3 ENGL 2210, World Literature 3 HIST 2610, United States History to 1865{5} 3 Laboratory Science{3} 4 PHED 1000, Scientific Principles and Practices of Health-Related Fitness, or DANC 1100, Stress Reduction Through Movement 2-3 Total 18-19 SPRING HOURS MATH 2520, Real Analysis II 3 MATH 2700, Linear Algebra and Vector Geometry 3 ENGL 2220, World Literature 3 HIST 2620, United States History Since 1865{5} 3 Laboratory Science{3} 4 Understanding of Ideas and Values{6}* 3 Total 19 JUNIOR YEAR FALL HOURS MATH 3510, Introduction to Abstract Algebra I{7} 3 MATH 4610, Probability 3 PSCI 1040, American Government 3 PHIL{8} 3 Minor Concentration{9} 6 Total 18 SPRING HOURS MATH 3410, Differential Equations I 3 MATH 4500, Introduction to Topology 3 PSCI 1050, American Government 3 Minor Concentration 6 Communications{10} 3 Total 18 SENIOR YEAR FALL HOURS MATH 4520, Introduction to Functions of a Complex Variable 3 MATH (Groups A, B, or C) 3 Minor Concentration 6 Visual and Performing Arts{11} 3 Total 15 SPRING HOURS MATH (Groups A, B, or C) 6 Minor Concentration 9 Understanding of Ideas and Values{6}* 3 Total 18 Total Minimum Hours Required: 130 Note: Some courses may require prerequisites not listed in the above plan. {1} Students should consult the Department of Mathematics for proper placement into the appropriate level before beginning their mathematics program. {2} Contact the Department of Foreign Languages and Literatures for proper placement into the appropriate level. Students must demonstrate proficiency by exam or complete the required prerequisites (LANG 1010- 1020) before enrolling in LANG 2040 or 2050. {3} Mathematics majors must complete two courses of natural/life science in the same discipline, either BIOL 1610-1630 and 1620-1640, or GEOL 1610 and 1620. They also must complete two courses of physical science in the same discipline, either CHEM 1410-1430 and 1420-1440, or PHYS 1710-1730 and 2220-2240. {4} Students who plan to take ENGL 2700 in place of ENGL 1320 should follow this sequence: ENGL 1310, 2210, 2220, 2700. {5} Advanced American/Texas History courses may be substituted to help meet the 42 advanced hours degree requirement. {6} Understanding of Ideas and Values: One course per group from any two of Groups I, II, III. See "University Core Curriculum Requirements" in the Academics section of this catalog for a list of approved courses. {7} 2.0 GPA required in all mathematics courses above MATH 3150. {8} PHIL 2050, 2310, or 2330 also will satisfy 3 hours of the Understanding of Ideas and Values, Group I requirement. See "Arts and Sciences Core Curriculum" in the College of Arts and Sciences section of this catalog. {9} Check with your academic adviser for an approved list of concentrations and approved course listings. {10} Proficiency exam or COMM 1010, 1440, or 2040. {11} See "University Core Curriculum Requirements" in the Academics section of this catalog for a list of approved Visual and Performing Arts courses. Note: ART 1300, 2350 may not be used to satisfy both the Visual and Performing Arts requirement and the Understanding of Ideas and Values, Group II requirement. * Taking courses in the minor and core at the advanced level will aid the student in reaching the 42 advanced hours necessary for graduation. Additional advanced elective courses may be required if this course is not chosen at the advanced level. The student is responsible for reaching 42 total advanced hours. See your faculty adviser each semester for help in program decisions and preparation for enrollment. Minor in Mathematics Students planning to minor in mathematics should consult the chair of the mathematics department. A minor consists of at least 18 hours and usually includes MATH 1710, 1720, 1780 or 2700, and 2730 or 2770, plus 6 advanced hours. MATH 3130, 3140, and 3150 may not be included in the minor, except for elementary education majors. Teacher Certification Students who expect to teach mathematics in secondary schools must complete the requirements of the state of Texas for teacher certification as listed by the Department of Teacher Education and Administration in the College of Education section. Students should consult the chair of the mathematics department for assistance in planning their program of study. Graduate Degrees The department offers degree programs leading to the Master of Arts, Master of Science and Doctor of Philosophy. For information, consult the Graduate Catalog. Scholarships and Financial Assistance The department administers two scholarship funds: the E.H. Hanson Scholarship and the Mildred Masters McCarty Scholarship. Jobs as tutors and graders also are available for mathematics majors. Contact the mathematics department office for information and application forms. Courses of Instruction All Courses of Instruction are located in one section at the back of this catalog.