|
Mathematics The department offers a certificate in Actuarial Studies. For further information refer to the Certificate section at the end of the College of Arts and Sciences’ section.
An undergraduate student may major in Mathematics or in Mathematical Sciences. The Bachelor’s degree in Mathematics emphasizes a deeper study of pure mathematics in the traditional mode. A student planning to continue into graduate study should major in Mathematics. The Mathematical Sciences degree offers an alternative involving more breadth. The mathematical requirements, which are fewer and tend to be more applied, are supplemented by additional requirements in computer science and applied statistics. Bachelor of Science in Mathematical Sciences Degree Program Hours: 120 Lower Division Preparation To qualify for admission to the program, FIU undergraduates must have met all the lower division requirements including CLAST, completed 60 semester hours, and must be otherwise acceptable into the program. Required Courses Common Prerequisites
Completion of two of the following courses with labs:
Courses required for the degree:
Upper Division Program Required Courses
In addition, two courses from the following list:
Electives The balance of the 60 semester hour requirement for graduation may be chosen from any courses in the University approved by the student’s advisor. Remarks: The following courses are not acceptable for credit toward graduation, unless a student has passed the course before declaring a Mathematical Sciences major: MAC 2233, STA 1013, STA 3122-23, STA 2023, and QMB 3150 (College of Business Administration). Minor in Mathematical Sciences Required Courses MAC 2311-2-3. Calculus I,II,III (or equivalent). Plus MAP 2302, MAS 3105, and two courses from those approved for the Mathematical Sciences Major program. A grade of ‘C’ or higher is necessary for the minor. Remarks: Courses completed elsewhere may be applied to the Mathematical Sciences minor, with the approval of the department. However, at least 2 of the 4 courses noted above, excluding MAC 2311-2-3, must be completed at FIU. Bachelor of Science in Mathematics Degree Program Hours: 120 Lower Division Preparation To qualify for admission to the program, FIU undergraduates must have met all the lower division requirements including CLAST, completed 60 semester hours, and must be otherwise acceptable into the program. Required Courses Common Prerequisites
Completion of two of the following courses with labs:
Courses required for the degree:
Upper Division Program Required Courses
In addition, three courses from each of the following lists. List 1
List 2
Electives The balance of the 60 semester hour requirement for graduation may be chosen from any courses in the University approved by the student’s advisor. Remarks: The following courses are not acceptable for credit toward graduation, unless a student has passed the course before declaring a Mathematics major: MAC 2233, STA 1013, STA 3122-23, STA 2023, and QMB 3150 (College of Business Administration). Combined BS in Mathematics/MS in Mathematical Sciences This program will allow strong students in mathematics to complete a bachelor’s degree and a master’s degree in 5 years rather than the usual six. A minimum of 140 credits are required for graduation with both the bachelor’s and the master’s degree. In addition to fulfilling the requirements for the Bachelor’s degree in mathematics, these 140 credits include 30 graduate credits required for the Master’s of Science in Mathematical Sciences. A maximum of ten (10) graduate mathematics credits can be concurrently used toward the bachelor’s and master’s degrees. All doubled counted courses must be at the 5000 level or higher. The combined BS/MS program has been designed to be a continuous program. However, upon completion of all the requirements of the undergraduate program, students will receive their BS degrees. Admission Requirements
Completion Requirements Year 1 and 2:
Year 3 Fall
Spring
One course from List 1 or 2
Summer One course from List 1 or 2 and 1 graduate course Year 4 Fall
One course from List 1 or 2 Senior Seminar (1 credit) Spring One graduate course Two courses from List 1 or 2 Summer Three graduate credits Year 5 Fall Nine graduate credits Spring Nine graduate credits The graduate courses distribution should follow catalog descriptions of the master’s program requirements. Students must take at least 3 courses from List 1 and at least 3 courses from List 2. The balance of the 140 semester hours required for graduation may be chosen from any courses in the university, a minimum of six (6) of these should be at the upper division level or higher. List 1
List 2
Minor in Mathematics Required Courses MAC 2311-2-3 Calculus I-I-III (or equivalent). Plus four courses from those approved for the Mathematics Major program. MAP 2302 and MAS 3105 may be included among these four courses. A grade of ‘C’ or higher is necessary for the minor. Remarks: Courses completed elsewhere may be applied to the Mathematics minor, with the approval of the department. However, at least 2 of the 4 courses noted above, excluding MAC 2311-2-3, must be completed at FIU. Certificate in Actuarial Studies The department offers a certificate in Actuarial Studies. For further information refer to the Certificate section at the end of the College of Arts and Sciences’ section. Course Descriptions Definition of Prefixes MAA-Mathematics, Analysis; MAC-Mathematics, Calculus and Pre-Calculus; MAD-Mathematics, Discrete; MAP-Mathematics, Applied; MAS-Mathematics, Algebraic Structures; MAT-Mathematics, General; MGF-Mathematics, General and Finite; MHF-Mathematics, History and Foundations; MTG- Mathematics, Topology and Geometry. F-Fall semester offering; S-Spring semester offering; SS-Summer semester offering. MAA 3200 Introduction to Advanced Mathematics (3). Topics include: naive set theory, functions, cardinality, sequences of real numbers and limits. Emphasis on formal proofs. Prerequisite: MAC 2313. (F) MAA 4211 Advanced Calculus (3). An intense study of the foundations of calculus. Topics may include: the real number system, continuity, differentiation, Riemann-Stieltjes integration, and series of functions. Note: The student must complete MAA 3200 before attempting this course. Prerequisites: MAC 2313, MAS 3105 and MAA 3200. (S) MAA 4212 Advanced Calculus II (3). A sequel to MAA 4211. Topics may include: theory of integration; analysis in several variables; and Fourier series. Prerequisite: MAA 4211. MAA 4402 Complex Variables (3). An introduction to complex variables, beginning with the algebra and geometry of the complex number system. Topics include: complex functions; analytic functions; Cauchy’s theorem and its consequences; Taylor and Laurent series; residue calculus; evaluation of real integrals and summation of series; conformal mapping. Prerequisites: MAC 2313, and MAP 2302 or MAA 4211. (F) MAC 1105 College Algebra (3). Operations on polynomials, rational expressions, radicals; lines, circles; inverse functions, exponential and logarithmic functions; systems of equations and inequalities. Students cannot receive credit for both this course and MAC 2147. Prerequisites: High school algebra and adequate placement test score. (F,S,SS) MAC 1114 Trigonometry (3). Trigonometric functions, identities, conditional equations, polar coordinates, vectors, polar graphs, complex numbers, DeMoivre’s Theorem, conic sections. Student cannot receive credit for both this course and MAC 2147 Precalculus. Prerequisite: Grade of “C” or higher in College Algebra. (F,S,SS) MAC 2147 Pre-calculus Mathematics (4). Topics to be covered include: functions, exponential and logarithmic functions, trigonometry and the basics of analytic geometry. Prerequisites: Two years of high school algebra and adequate placement test score. (F,S,SS) MAC 2233 Calculus For Business (3). A one semester introduction to the basic notions of calculus. Specific topics include: Differential Calculus using polynomial, exponential and logarithmic functions, and its application to optimization; integral calculus with area and probability applications. Prerequisites: Grade of “C” or higher in College Algebra or Precalculus or adequate placement test score. (F,S,SS) MAC 2311 Calculus I (4). Limits, derivatives and their formulas, applications of derivatives, introduction to anti derivatives, introduction to parametric curves. Prerequisites: Grade of “C” or higher in Trigonometry or Precalculus or adequate placement test score. (F,S,SS) MAC 2312 Calculus II (4). Applications of the integral, integration techniques, improper integrals, Riemann sums, the integral, Fundamental Theorem of Calculus, infinite series, Taylor series, polar coordinates, parametric equations. Prerequisites: Grade of “C” or higher in Calculus I or AP Calculus credit. (F,S,SS) MAC 2313 Multivariable Calculus (4). This course deals with the differential and integral calculus of real valued multivariable functions. The topics include: directional and partial derivatives, gradients, and their applications; differential calculus of vector valued functions; multiple, iterated, line, and surface integrals. Prerequisites: MAC 2312 or equivalent with a grade of ‘C’ or better. (F,S,SS) MAD 1100 Mathematics for Information Technology (3). Introduction to discrete mathematical structures with emphasis on applications to information technology: binary numbers, logic, sets, functions, recursion, combinatories, graph theory, Boolean algebra. Prerequisite: College Algebra. MAD 2104 Discrete Mathematics (3). Sets, functions, relations, permutations, and combinations, propositional logic, matrix algebra, graphs and trees, Boolean algebra, switching circuits. (F,S,SS) MAD 3305 Graph Theory (3). An introduction to the study of graphs. Topics include the following: paths and circuits, connectedness, trees, shortest paths, networks, planar graphs, the coloring of graphs, and directed graphs. Applications of graphs to computer science will be discussed. Prerequisites: COP 2210 or CGS 2420 and either MAS 3105 or MAD 2104. (F,S,SS) MAD 3401 Numerical Analysis (3). Basic ideas and techniques of numerical analysis. Topics include: finite differences, interpolation, solution of equations, numerical integration and differentiation, applications, introduction to applied linear algebra. This course will make extensive laboratory use of the computer facility. Prerequisites: COP 2210 or CGS 2420 and MAC 2312. (F,S,SS) MAD 3512 Theory of Algorithms (3). Strings, formal languages, finite state machines, Turing machines, primitive recursive and recursive functions, recursive unsolvability. Prerequisite: MAD 2104. Computer Science majors must also take COT 3420. (F,S,SS) MAD 4203 Introduction to Combinatorics (3). A survey of the basic techniques of combinatorial mathematics. Topics will include the Pigeonhole Principle, Binomial Coefficients, Inclusion-Exclusion, Recurrence Relations, and Generating Functions. Prerequisites: MAC 2313 or both MAC 2312 and MAD 2104. (SS) MAP 2302 Differential Equations (3). An introduction to differential equations and their applications, based upon a knowledge of calculus. Topics to include: initial value problems of the first order, numerical solutions, systems of differential equations, linear differential equations, Laplace transforms, series solutions. Prerequisite: MAC 2312 with a grade of ‘C’ or better. (F,S,SS) MAP 3103 Mathematical Modeling and Applications (3). A course to provide an understanding of the use of mathematical models in the description of the real world. Basic principles in the philosophy of formal model building as well as specific models will be considered. Prerequisites: MAS 3105 and either MAC 2313 or MAP 2302. MAP 3103L Lab for Mathematical Modeling (1). Lab sessions complement the course of mathematical modeling (MAP3103). Computer projects using "MATLAB" will be used. Prerequisite: MAC 2313. Corequisite: MAP 3103. MAP 3104 Topics in Mathematical Modeling (3). A sequel to MAP 3103. In-depth study of techniques listed for MAP 3103. Prerequisite: MAP 3103. MAP 4401 Advanced Differential Equations (3). A second course in differential equations. Topics may include: Bessel functions and other special functions arising from classical differential equations, Sturm-Liouville problems, partial differential equations, transform techniques. Prerequisites: MAP 2302 and MAC 2313. (S) MAP 4401L Lab for Advanced Differential Equations (1). Lab sessions complement the course of advanced differential equations (MAP4401). Computer projects using "MATLAB" will be used. Prerequisites: MAP 2302, MAC 2313. Corequisite: MAP 4401. MAS 3105 Linear Algebra (3). An introduction to the topics in linear algebra most often used in applications. Topics include: matrices and their applications; simultaneous linear equations and elementary operations; linear dependence; vector spaces; rank and inverses; inner products and ‘best’ approximations; numerical solutions of simultaneous linear equations; eigen-values and eigenvectors; iterative methods for calculating eigenvalues; and systems of linear equations. Prerequisite: MAC 2312. (F,S,SS) MAS 3931 Topics in Actuarial Mathematics (1). Topics related to calculus/linear algebra such as mono-tone sequences, least upper bound, complex arithmetic, solid analytic geometry, linear transformations. Mathematics involved in insurance. Prerequisite: Admission to Actuarial Studies Certificate program. MAS 4203 Number Theory (3). Topics to be discussed are selected from the following: congruences, Diophantine equations, distribution of primes, primitive roots, quadratic reciprocity, and classical theorems of number theory. Prerequisites: MAA 3200 or MAS 3105 or MTG 3212. (SS) MAS 4301 Algebraic Structures (3). An introduction to abstract mathematical structures of modern algebra. Fundamental concepts of groups, rings, and fields will be studied. Note: the student must complete MAA 3200 before attempting this course. Prerequisites: MAS 3105 and MAA 3200. (S) MAS 4302 Topics in Algebraic Structures (3). A sequel to Algebraic Structures. Topics may include: a continuation of the study of groups, rings and/or fields; polynomial domains; Euclidean domains; and Galois theory. Prerequisite: MAS 4301. MAT 2949 Cooperative Education in Mathematical Sciences (1-3). One semester of full-time supervised work in an outside organization taking part in the University Coop program. A written report and supervisor evaluation will be required of each student. Prerequisites: Calculus I and COP 2210. MAT 3905 Independent Study (VAR). Individual conferences, assigned readings, and reports on independent investigations. MAT 3930 Special Topics (VAR). A course designed to give groups of students an opportunity to pursue special studies not otherwise offered. MAT 3949 Cooperative Education in Mathematical Sciences (1-3). One semester of full-time supervised work in an outside organization taking part in the University Coop Program. Limited to students admitted to the Co-op Program. A written report and supervisor evaluation will be required of each student. Prerequisites: Calculus II and COP 2210. MAT 4905 Independent Study (VAR). Individual conferences, assigned readings, and reports on independent investigations. MAT 4930 Special Topics (VAR). A course designed to give groups of students an opportunity to pursue special studies not otherwise offered. MAT 4934 Senior Mathematics Seminar (1). An exploration of research topics in the student's subfield. Coursework will include a written report, oral presentation, and departmental major field test. Prerequisite: Senior standing. MAT 4943 Mathematical Sciences Internship (VAR). A special program to encourage students to get on-the-job experience in computer sciences, statistics, or mathematics in an industrial enterprise, governmental agency or other organization. Requirements: minimum grade of ‘B’ or higher in all courses in the major area, and approval by Departmental Internship Committee. Application is required at least one term in advance of registration for this course. MAT 4949 Cooperative Education in Mathematical Sciences (1-3). One semester of full-time supervised work in an outside organization taking part in the University Coop Program. Limited to students admitted to the Co-op Program. A written report and supervisor evaluation will be required of each student. Prerequisites: Calculus II, a statistics course, and COP 2210. MGF 1106 Finite Mathematics (3). Study of concepts and applications involving finite mathematical processes such as sets, combinatorial techniques, formal logic, discrete probability, linear systems, matrices, linear programming. Prerequisite: Working knowledge of high school algebra. (F,S,SS) MGF 1107 The Mathematics of Social Choice and Decision Making (3). Voting systems and their desirable properties. Weighted voting systems, fair division procedures, apportionment methods and game theory. MHF 3404 History of Mathematics (3). Development of mathematical thought through the ages. Topics may include equation solving, trigonometry, astronomy, and calculus. Prerequisite: MAC 2312. (S) MHF 4102 Axiomatic Set Theory (3). Axioms of set theory, order and well-foundedness, cardinal numbers, ordinal numbers, axiom of choice, special topics. Prerequisites: MAA 3200 or permission of the instructor. (S, alternate years) MHF 4302 Mathematical Logic (3). A study of formal logical systems and their applications to the foundations of mathematics. Topics to be selected from the following: definition of mathematical proofs; set theory; analysis formalized with the predicate calculus; theorem of Godel and Church; recursive function theory; and idealized computers. Prerequisites: MAA 3200 or MAD 3512. (S, alternate years) MHF 4401 Topics in the History of Modern Mathematics (3). Riemannian geometry, relativity and other topics at discretion of instructor. Prerequisites: MAC 2313, MAS 3105. MTG 1204 Geometry for Education (3). Introduction for teachers to basic concepts of Euclidean geometry with ideas and activities adaptable to classroom. Students study and analyze pattern, learning and enhancing analytic, creative and visualization skills. MTG 3212 College Geometry (3). A study of the basic structure of Euclidean geometry together with topics from advanced Euclidean geometry and non-Euclidean geometry. Prerequisites: Calculus II or permission of the instructor. (S) MTG 4254 Differential Geometry (3). Hypersurfaces in Rⁿ. Geodesics and curvature. Parametrisation of surfaces, abstract manifolds. Integration, surfaces with boundary, Stokes Theorem. Isometries and intrinsic geometry. Gauss-Bonnet Theorem. Prerequisites: MAC 2311, MAS 3105, MAP 2302 or permission of the instructor. MTG 4302 Topology (3). An introductory course in topology requiring a prerequisite knowledge of calculus. Topics to be discussed will be selected from the following: topological spaces, metric spaces, continuity, completeness, compactness, separation axioms, products spaces, subspaces, convergence, and homotopy theory. Prerequisites: MAC 2313, MAS 3105, and MAA 3200. (SS) STA 4603-STA 4604 Mathematical Techniques of Operations Research I and II (3-3) . An introduction to those topics in mathematics associated with studies in operations research. Topics include the following: linear programming and related topics, dynamic programming, queuing theory, computer simulation, network analysis, inventory theory, decision theory, integer programming. Prerequisites: MAS 3105 and either STA 3033 or STA 4322. | College of Arts and Sciences
|