2005-06 Undergraduate Catalog
Majors
Students who intend to major in mathematics or in quantitative sciences should consult a department adviser.
General Education: Students not majoring in mathematics or quantitative sciences should refer to the critical-tracking criteria and other requirements for their majors in order to determine appropriate course(s) to take. Precalculus, calculus, and many higher-level courses meet General Education requirements. For students whose majors require no specific math course, MGF 1106 and MGF 1107 are appropriate General Education math courses.
Placement: Students with strong math backgrounds who plan to take a calculus or higher-level course should consult an adviser about placing into the appropriate course.
Students who must take Calculus 1 and whose high-school math background is weak should begin with one of the precalculus courses: MAC 1147, MAC 1140 or MAC 1114. MAC 1147 is a fast-paced review of pre-calculus algebra and trigonometry. The combination of MAC 1140 (Precalculus Algebra) and MAC 1114 (Trigonometry) covers the same material as MAC 1147, but at a slower pace.
A background in trigonometry is necessary for MAC 2311 but not for MAC 2233. Therefore MAC 1140 provides sufficient background for MAC 2233, but students planning to take a UF precalculus course to prepare for MAC 2311 should take MAC 1147 or both MAC 1140 and MAC 1114.
Students who need to take a precalculus or Calculus 1 course are strongly advised (and in some cases required) to take the online Calculus Readiness Assessment; refer to the Academic Advising section of this catalog and
www.math.ufl.edu/courses/advising/ready_for_calculus.html
www.math.ufl.edu/courses/advising/around_calculus.html
www.math.ufl.edu/courses/advising/recalculus.html
Additional help also is available at the Academic Advising Center and the Mathematics Department office in Little Hall, Room 358.
Combined Degree Program in Mathematics: BS or BA / MA or MS (non-thesis only). Contact the undergraduate coordinator in the Department of Mathematics, 358 Little Hall, for details or refer to www.math.ufl.edu/undergradprog.
The Bachelor of Science (B.S.) program is intended for students who wish to pursue graduate study in mathematics, as well as for other strong students with a deep interest in mathematics.
The Bachelor of Arts (B.A.) program is intended for students who may wish to pursue a career in a mathematical field or to teach mathematics at the secondary-school level, but who do not currently contemplate graduate study in mathematics.
Students pursuing the B.A. degree have greater flexibility in their choice of electives, facilitating the possibility of a double-major with another scientific discipline.
For each degree, students are required to take eight core courses, providing a broad base in mathematics, and four electives chosen from a list of approved courses. All but two of the core courses are the same for both degrees.
Students wishing to pursue graduate study in a Ph.D. program in mathematics are strongly urged to complete MAS 4301 and MAA 4211-4212 by the end of their junior years and to include MAS 5311 (Introductory Algebra 1) and MAA 4226 (Modern Analysis 1) among their electives, and are encouraged to take more than four electives.
Students who plan to teach secondary-school mathematics are advised to include MTG 3212 (Geometry) among their electives.
Students who plan to teach secondary-school mathematics are advised to include MTG 3212 (Geometry) among their electives.
All math majors are encouraged to meet the college distribution requirement in the physical sciences with the sequence PHY 2048-2049 (Physics with Calculus) or the sequence PHY 2060-2061 (Enriched Physics with Calculus).
Math majors also should take no mathematics course at the 3000 level or below that is not on the list of core courses or on the list of approved electives, except with adviser approval.
Students who wish to pursue a career in applied mathematics are urged to take STA 4322 and a computer-science course that covers C or C++; note that these courses may have prerequisites.
All math majors are required to take:
Any of the following courses offered outside the mathematics department:
The semester-by-semester plans below are only sample programs; they may be adjusted to reflect background and goals. Critical-tracking courses do not necessarily have to be completed as early as in the sample programs; see the tracking criteria above. Consult a department adviser (in 358 Little Hall) early to plan your individual program.
| Mathematics |
| College: Liberal Arts and Sciences |
| Degrees: Bachelor of Science in Mathematics, Bachelor of Arts in Mathematics |
|
Bachelor of Science in Quantitative Sciences (Refer to Quantitative Sciences for more information on this degree.) |
| Hours for the Degree: 120 |
| Minor: Yes |
| Combined-Degree Program: Yes |
| Website: www.math.ufl.edu |
Students who intend to major in mathematics or in quantitative sciences should consult a department adviser.
General Education: Students not majoring in mathematics or quantitative sciences should refer to the critical-tracking criteria and other requirements for their majors in order to determine appropriate course(s) to take. Precalculus, calculus, and many higher-level courses meet General Education requirements. For students whose majors require no specific math course, MGF 1106 and MGF 1107 are appropriate General Education math courses.
Placement: Students with strong math backgrounds who plan to take a calculus or higher-level course should consult an adviser about placing into the appropriate course.
Students who must take Calculus 1 and whose high-school math background is weak should begin with one of the precalculus courses: MAC 1147, MAC 1140 or MAC 1114. MAC 1147 is a fast-paced review of pre-calculus algebra and trigonometry. The combination of MAC 1140 (Precalculus Algebra) and MAC 1114 (Trigonometry) covers the same material as MAC 1147, but at a slower pace.
A background in trigonometry is necessary for MAC 2311 but not for MAC 2233. Therefore MAC 1140 provides sufficient background for MAC 2233, but students planning to take a UF precalculus course to prepare for MAC 2311 should take MAC 1147 or both MAC 1140 and MAC 1114.
Students who need to take a precalculus or Calculus 1 course are strongly advised (and in some cases required) to take the online Calculus Readiness Assessment; refer to the Academic Advising section of this catalog and
www.math.ufl.edu/courses/advising/ready_for_calculus.html
www.math.ufl.edu/courses/advising/around_calculus.html
www.math.ufl.edu/courses/advising/recalculus.html
Additional help also is available at the Academic Advising Center and the Mathematics Department office in Little Hall, Room 358.
Combined Degree Program in Mathematics: BS or BA / MA or MS (non-thesis only). Contact the undergraduate coordinator in the Department of Mathematics, 358 Little Hall, for details or refer to www.math.ufl.edu/undergradprog.
Comparison of Bachelor of Science and Bachelor of Arts programs in Mathematics
The Bachelor of Science (B.S.) program is intended for students who wish to pursue graduate study in mathematics, as well as for other strong students with a deep interest in mathematics.
The Bachelor of Arts (B.A.) program is intended for students who may wish to pursue a career in a mathematical field or to teach mathematics at the secondary-school level, but who do not currently contemplate graduate study in mathematics.
Students pursuing the B.A. degree have greater flexibility in their choice of electives, facilitating the possibility of a double-major with another scientific discipline.
For each degree, students are required to take eight core courses, providing a broad base in mathematics, and four electives chosen from a list of approved courses. All but two of the core courses are the same for both degrees.
Bachelor of Science program
Core courses
- Calculus 2 (MAC 2312 or 2512 or 3473),
- Calculus 3 (MAC 2313 or 3474),
- Differential Equations (MAP 2302),
- Numbers and Polynomials (MAS 3300) or Sets and Logic (MHF 3202),
- Linear Algebra 1 (MAS 4105),
- Abstract Algebra 1 (MAS 4301), and
- The sequence Advanced Calculus 1 and 2 (MAA 4211 and 4212).
- The requirement of MAS 3300 or MHF 3202 may be waived for students who present evidence of significant prior experience in writing proofs of theorems.
- The four electives must be chosen from the list of approved electives below, and at least three must be courses offered by the mathematics department at the 4000-level or above.
Students wishing to pursue graduate study in a Ph.D. program in mathematics are strongly urged to complete MAS 4301 and MAA 4211-4212 by the end of their junior years and to include MAS 5311 (Introductory Algebra 1) and MAA 4226 (Modern Analysis 1) among their electives, and are encouraged to take more than four electives.
Students who plan to teach secondary-school mathematics are advised to include MTG 3212 (Geometry) among their electives.
Bachelor of Arts program
Core courses
- Calculus 2 (MAC 2312 or 2512 or 3473),
- Calculus 3 (MAC 2313 or 3474),
- Differential Equations (MAP 2302),
- Numbers and Polynomials (MAS 3300) or Sets and Logic (MHF 3202),
- Linear Algebra 1 (MAS 4105),
- Abstract Algebra (MAS 4301), and
- The sequence Advanced Calculus for Engineers and Physical Scientists 1 and 2 (MAA 4102 and 4103).
- The requirement of MAS 3300 or MHF 3202 may be waived for students who present evidence of significant prior experience in writing proofs of theorems.
- The four electives must be chosen from the list of approved electives below, and at least one must be a course offered by the mathematics department at the 4000-level or above.
Students who plan to teach secondary-school mathematics are advised to include MTG 3212 (Geometry) among their electives.
For both the B.S. and B.A. degrees
All math majors are encouraged to meet the college distribution requirement in the physical sciences with the sequence PHY 2048-2049 (Physics with Calculus) or the sequence PHY 2060-2061 (Enriched Physics with Calculus).
Math majors also should take no mathematics course at the 3000 level or below that is not on the list of core courses or on the list of approved electives, except with adviser approval.
Students who wish to pursue a career in applied mathematics are urged to take STA 4322 and a computer-science course that covers C or C++; note that these courses may have prerequisites.
All math majors are required to take:
- Eight core courses, providing a broad base in mathematics, and
- Four electives chosen from a list of approved courses.
- All but two of the core courses are the same for both degrees.
Approved electives for all mathematics majors:
- MAD 3107 Discrete Mathematics
- MTG 3212 Geometry
- MHF 3404 History of Mathematics
- MAA 4226 Introduction to Modern Analysis 1
- MAA 4227 Introduction to Modern Analysis 2
- MAA 4402 Functions of a Complex Variable
- MAD 4203 Introduction to Combinatorics 1
- MAD 4204 Introduction to Combinatorics 2
- MAD 4401 Introduction to Numerical Analysis
- MAS 4107 Linear Algebra 2
- MAS 4124 Introduction to Numerical Linear Algebra
- MAS 4302 Abstract Algebra 2
- MAS 4156 Introduction to Vector Analysis (will not count toward math major if PHY 3323 or PHY 4324 is taken)
- MAS 4203 Introduction to Number Theory
- MAP 4305 Differential Equations for Engineers and Physical Scientists
- MAP 4341 Elements of Partial Differential Equations
- MAP 4413 Fourier Series and Transforms 1
- MAP 4102 Probability and Stochastic Processes 2
- MAT 4930 Special Topics in Mathematics (only if approved by Undergraduate Coordinator)
- MHF 4102 Elements of Set Theory
- MHF 4203 Foundations of Mathematics
- MTG 4302 Introduction to Topology 1
- MTG 4303 Introduction to Topology 2
- Any course offered by the mathematics department at the 5000-level or above (with the exception that MAS 5157 will not count toward the math major if PHY 3323 or PHY 4324 is taken), and
Any of the following courses offered outside the mathematics department:
- COP 3530 Data Structures and Algorithm
- CDA 3101 Introduction to Computer Organization
- COP 4600 Operating Systems
- ESI 4312 Operations Research 1
- ESI 4313 Operations Research 2
- PHY 3062 Honors Physics 3
- PHY 3063 Enriched Modern Physics
- PHY 3221 Mechanics 1
- PHY 3323 Electromagnetism 1
- PHY 3513 Thermal Physics 1
- PHY 4222 Mechanics 2
- PHY 4324 Electromagnetism 2
- PHY 4328 Classical Electrodynamics
- PHY 4422 Optics 1
- PHY 4523 Statistical Physics
- PHY 4604 Introductory Quantum Mechanics 1
- PHY 4605 Introductory Quantum Mechanics 2
- STA 4321 Mathematical Statistics 1
- STA 4322 Mathematical Statistics 2
- STA 4210 Regression Analysis
- STA 4211 Design of Experiments
- STA 4853 Introduction to Time Series and Forecasting
Critical-tracking requirements for the B.S. and B.A. degrees in Mathematics. All students must meet these criteria to remain 'on track' for the major.
Critical Tracking Requirements
Semester 1:
- Achieve 2.0 UF GPA
- Complete MAC 2311
Semester 2:
- Complete MAC 2312
- Maintain 2.0 UF GPA
Semester 3:
- Complete MAC 2313
- Maintain 2.0 UF GPA
Semester 4:
- Complete MAP 2302 with a 2.5 GPA on all critical-tracking course work
- Maintain 2.0 UF GPA
Semester 5:
- Complete MAS 3300 or MHF 3202 with a 2.5 GPA on all critical-tracking course work
- Maintain 2.0 UF GPA
The semester-by-semester plans below are only sample programs; they may be adjusted to reflect background and goals. Critical-tracking courses do not necessarily have to be completed as early as in the sample programs; see the tracking criteria above. Consult a department adviser (in 358 Little Hall) early to plan your individual program.
Semesters 1–4 are the same for both the B.S. and B.A. degrees
| Semester 1 | Credits |
| MAC 2311 Analytic Geometry and Calculus 1 (GE–M) | 4 |
| Biological Sciences (GE) | 3 |
| Social and Behavioral Sciences (GE) | 3 |
| Humanities (GE) | 3 |
| Total | 13 |
| Semester 2 | Credits |
| MAC 2312 Analytic Geometry and Calculus 2 (GE–M) | 4 |
| Biological Sciences (GE) | 3 |
| Composition (GE) | 3 |
| Humanities (GE) | 3 |
| Elective | 3 |
| Total | 16 |
| Semester 3 | Credits |
| MAC 2313 Analytic Geometry and Calculus 3 (GE–M) | 4 |
| MAS 3300 Numbers and Polynomials | 3 |
| Physical Sciences (GE) | 3 |
| Science laboratory (GE–P or B) | 1 |
| Social and Behavioral Sciences (GE) | 3 |
| Humanities (GE) | 3 |
| Total | 17 |
| Semester 4 | Credits |
| MAP 2302 Elementary Differential Equations (GE–M) | 3 |
| MAS 4105 Linear Algebra 1 | 4 |
| Physical Sciences (GE) | 3 |
| Composition | 3 |
| Social and Behavioral Sciences (GE) | 3 |
| Total | 16 |
Students pursuing the B.S. degree
| Semester 5 | Credits |
| MAS 4301 Abstract Algebra 1 | 3 |
| MAA 4211 Advanced Calculus 1 | 3 |
| Foreign language | 4-5 |
| Elective (3000 level or higher, not in major) | 3 |
| Total | 13-14 |
| Semester 6 | Credits |
| MAA 4212 Advanced Calculus 2 | 3 |
| Foreign language | 3-5 |
| Mathematics elective | 3 |
| Elective (3000 level or higher, not in major) | 3-4 |
| Elective | 3-0 |
| Total | 15 |
| Semester 7 | Credits |
| MAA 4226 Introduction to Modern Analysis 1 or another math elective | 3 |
| MAS 5311 or another math elective | 3 |
| Two electives (3000 level or higher, not in major) | 6 |
| Elective (or foreign language if 4-3-3 option) | 3 |
| Total | 15 |
| Semester 8 | Credits |
| MAA 4227 Introduction to Modern Analysis 2 or another math elective | 3 |
| Mathematics elective | 3 |
| Two electives (3000 level or higher, not in major) | 6 |
| Elective (inside or outside major) | 3 |
| Total | 15 |
Students pursuing the B.A. degree
| Semester 5 | Credits |
| MAS 4301 Abstract Algebra 1 | 3 |
| Mathematics elective | 3 |
| Foreign language | 4-5 |
| Elective (3000 level or higher, not in major) | 3 |
| Total | 13-14 |
| Semester 6 | Credits |
| Mathematics elective | 3 |
| Foreign language | 3-5 |
| Two electives (3000 level or higher, not in major) | 6 |
| Elective | 3-0 |
| Total | 15-14 |
| Semester 7 | Credits |
| MAA 4102 Introduction to Advanced Calculus for Engineers and Physical Scientists 1 | 3 |
| Mathematics elective | 3 |
| Two electives (3000-level or higher, not in major) | 6 |
| Elective (or foreign language if 4-3-3 option) | 3 |
| Total | 15 |
| Semester 8 | Credits |
| MAA 4103 Introduction to Advanced Calculus for Engineers and Physical Scientists 2 | 3 |
| Mathematics elective | 3 |
| Two electives (3000-level or higher, not in major) | 6 |
| Electives | 3 |
| Total | 15 |