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Recommendations Concerning Related Courses Departmental Requirements for Graduation Concentration BSc: General Study In Mathematics Concentration BSc/AM: General Study In Applied Mathematics Basic Curriculum in Mathematics Concentration C: Computing and Applied Mathematics Concentration GS: General Study in Mathematics Concentration GS/Am: General Study in Applied Mathematics Program M/E: Joint Major in Mathematics/Economics Concentration GS/ED: General Study in Mathematics and Education |
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Mathematics Department of Mathematics The Program
Students, including freshmen, considering majoring in mathematics are encouraged to consult as early as possible with the departmental director of undergraduate studies. Admission to the department as far in advance of graduation as possible ensures that the department and the student can plan together a program best suited to the student's needs. Transfer Policy Transfer students who intend to major in mathematics are urged to consult the director of undergraduate studies before or very early in their first semester at the University at Buffalo to determine equivalency of transferred mathematics courses. Transfer students are required to complete at least four upper-division courses in the Department of Mathematics at the University at Buffalo. Recommendations Concerning Related Courses The Department of Mathematics strongly recommends that its majors in the theoretically oriented concentrations (Concentrations GS and GS/AM or Concentrations BSc and BSc/AM) take at least two semesters of French, German, or Russian, since these, along with English, are the basic languages of the mathematical literature. All mathematicians need some facility with computers. The department, therefore, recommends that its students take an introductory course in scientific programming. Specifically, a one year sequence, CSE113-114 or CSE115-116, is strongly recommended for students majoring in mathematics. Some major concentrations have specific computer science requirements. Acceptance Criteria Applicants to the mathematics program should bring a copy of their current UB DARS reports directly to the Department of Mathematics. Students may apply at any time after they have completed the three-course calculus sequence MTH141-142-241 or the equivalent at a transfer institution, but should apply, if possible, while enrolled in MTH241 to receive appropriate advisement. The department's requirement for admission is a 2.5 GPA in the three calculus courses. Students who have taken more than these three courses usually need a minimum grade of "C" in any additional required courses they have completed. Note: Admittance to the department guarantees admittance to the Basic Curriculum Program only-all other concentrations or programs require specific approval from the director of undergraduate studies. Students who expect difficulty in being admitted to the department should follow the requirements for the Basic Curriculum Program or see the director of undergraduate studies for advice on which concentration to follow, pending admittance. Departmental Probation Students whose math GPA drops below 2.0 will be placed on departmental probation for one semester. If their GPA remains below 2.0 at the end of the probationary semester, they will be dropped from the department. They may reapply after one semester. Departmental Requirements for Graduation After a student has been accepted as a major, progress toward fulfillment of the degree requirements is monitored by the department. A student will be recommended for a baccalaureate degree in mathematics only if (1) the program has been approved by the director of undergraduate studies; (2) all required/approved courses have been completed; and (3) minimum departmental GPA of 2.0 has been attained in the specific program. Mathematics (MTH) Note: Mathematics courses are not numbered according to difficulty. For example, MTH301 is a theoretically oriented course, stressing proofs. Some students find it to be much more difficult than MTH417 and MTH418. 115 Survey of Algebra and Trigonometry (4) (F; Sp) A pre-calculus course; covers topics from the NYS Regents Course III: order, absolute value, inequalities, exponents, radicals, polynomials, rational expressions, solving systems of linear equations, quadratic equations and inequalities, functions (rational, logarithmic, exponential, trigonometric), graphing, trigonometric identities. Applications to problems are emphasized throughout the course. This fast-paced course is designed to review Course III and prepare students for further courses in mathematics. Students with three years of high school math but with weak algebra skills should take ULC147 before MTH115. Students who have had only two years of high school mathematics may take MTH115, or may prefer to take a two-semester sequence covering this material more thoroughly and at a more moderate pace: ULC147 and ULC148. LEC/LAB 117 Applications of Mathematical Concepts (3) Prerequisite: two years of NYS Regents-level high school mathematics Intended to be non-technical, with an emphasis on conceptually sophisticated and aesthetically appealing mathematical discoveries of the twentieth century, such as mathematical aspects of social choice, management science, and growth and symmetry. LEC/REC 119 Survey of Finite Mathematics (4) Prerequisite: three years of NYS Regents-level high school mathematics Elementary topics in topology, probability, numerical sequences, and groups. LEC/LAB 121 Survey of Calculus and Its Applications I (4) (F; Sp) Prerequisite: NYS Regents Course III or MTH115 For students in social, biological, and management sciences. Limits, continuity, differentiation of algebraic and exponential functions; applications; introduction to integration. LEC/LAB 122 Survey of Calculus and Its Applications II (4) (F; Sp) Prerequisite: MTH121 or MTH131 with recommended grade of "C" or higher Continuation of MTH121. Maximization of functions of several variables using both calculus and elementary linear programming techniques. Elementary integration, simple differential equations, matrix algebra. LEC/LAB 131 Mathematical Analysis for Management (4) (F; Sp) Prerequisite: NYS Regents Course III or MTH115 For students in Management. Limits, continuity, differentiation of algebraic and exponential functions. Applications, partial derivatives and applications. Introduces integration. LEC/LAB/REC 141 College Calculus I (4) (F; Sp) Prerequisite: trigonometry or NYS Regents Course III or MTH115 Beginning of a three-semester sequence in calculus for students of mathematics, natural sciences, and engineering. Covers differentiation and integration with applications. LEC/LAB 142 College Calculus II (4) (F; Sp) Prerequisite: MTH141 with recommended grade of "C" or higher; MTH121 is usually not adequate preparation for MTH142 Differentiation and integration of transcendental functions; infinite sequences; series and power series; methods of integration; additional topics in analytic geometry. LEC/LAB 145 Introduction to Mathematical Computing and Programming (4) (F) Basic introduction to computers and computer organization; algorithms and their development in a structured manner; procedures and functions; programming; aspects and topics from computer science. Credit not given for both MTH145 and CSE113. LEC/LAB 151 Enriched Calculus I (4) (F) Prerequisites: permission of instructor and a math SAT score of at least 650 Similar to MTH141 but more challenging. May include additional material and more proofs. LEC/LAB 152 Enriched Calculus II (4) (Sp) Prerequisite: MTH151 or permission of instructor Continuation of MTH151. Covers all the material in MTH142 and additional material as described in MTH151. LEC/LAB 153 Honors Calculus I (4) (F) Prerequisite: permission of instructor or a score of 4 or 5 on the advanced placement calculus exam or equivalent. Credit may be given in addition to advanced placement credit First course in the honors sequence for intended math majors or for others with suitable preparation. Emphasizes proofs and concepts of calculus. LEC/LAB 154 Honors Calculus II (4) (Sp) Prerequisite: MTH153 or permission of instructor Continuation of MTH153. May be taken in addition to advanced placement credit. LEC/LAB 172 Principles of Mathematical Computing (4) (Sp) Prerequisite: MTH145 Programming through data structures (sorting algorithms) and applications in scientific computing. Credit is not given for both MTH172 and CSE114. LEC/LAB 181 Conceptual Mathematics I (3) Prerequisite: high school algebra Intended primarily for students not contemplating a major in the natural sciences, this course concentrates on the conceptual nature of mathematics, and should aid in understanding science as part of the general culture, as well as in learning to analyze and reason more clearly. It differs substantially from other beginning courses, which must emphasize the computational facility needed for advanced work. Topics include categories; adding and multiplying numbers, objects, and propositions; transformations of space and quantity. LEC/LAB 191 Introduction to Discrete Mathematics I (4) (F) Prerequisites: working knowledge of a programming language First part of a two-semester sequence intended to provide the mathematical foundations for the study of computer science. This course is also approved for mathematics majors in Concentration GS/ED. Topics include sets, relations, functions, mathematical induction, fundamental counting methods, difference equations, and sequences and series. Same as CSE191. LEC/LAB 192 Introduction to Discrete Mathematics II (4) (S) Prerequisite: MTH191 or CSE191 Second part of a two-semester sequence in discrete mathematics intended to provide the mathematical foundations for the study of computer science. Topics include discrete probability, mathematical logic, linear algebra, and graph theory. Same as CSE192. LEC/LAB 241 College Calculus III (4) (F; Sp) Prerequisite: MTH142 with recommended grade of "C" or higher Note: MTH121-122 is not adequate preparation for MTH241. Geometry and vectors of n-dimensional space; Green's theorem, Gauss theorem, Stokes theorem; multidimensional differentiation and integration; application to 2- and 3-D space. LEC/LAB 251 Honors Calculus III (4) (F) Prerequisite: permission of instructor Third-semester calculus course for honors students and students with an excellent record in previous calculus courses. Emphasizes proofs and concepts of calculus. LEC/LAB 272 Mathematics of Data Manipulation (4) (Sp) Prerequisite: MTH172 or CSE114 Aspects of data representation and manipulation needed for applications programming together with an introduction to their mathematical theory. LEC/LAB 301 Basic Analysis and Proofs (4) (F; Sp) Prerequisite: MTH241 Prerequisite for MTH431 and MTH335, and is recommended for MTH419. Introduces mathematical proofs. Problem solving and proof construction in the context of geometry of Rn, convergence, basic topological definitions in Rn, completeness, compactness (with emphasis on examples in R, R2, and R3). LEC/LAB 306 Introduction to Differential Equations (4) Prerequisite: MTH142 Analytic solutions, qualitative behavior of solutions to differential equations. First-order and higher-order ordinary differential equations, including nonlinear equations. Covers analytic, geometric, and numerical perspectives as well as an interplay between methods and model problems. Discusses necessary matrix theory and explores differential equation models of phenomena from various disciplines. Integrated into the course is the use of a mathematical software system designed to aid in the numerical and qualitative study of solutions, and to aid in the geometric interpretation of solutions. LEC/LAB 309 Introductory Linear Algebra (4) (F; Sp) Prerequisite: MTH142 or MTH192 or CSE192 Linear equations, matrices, determinants, vector spaces, linear mappings, inner products, eigenvalues, eigenvectors. LEC/LAB 310 Applications of Linear Algebra (4) (F; Sp) Prerequisites: MTH306, MTH309 Topics selected by the instructor. LEC/LAB 313 Elements of Set Theory (4) Prerequisite: MTH241 or permission of instructor Cardinals, ordinals, order-types, and operations on them. Axiom of choice. Sets. LEC/REC 314 Logic for Computer Science (3) (F) Prerequisites: at least one year of previous training in college mathematics and one year of programming Introduces the predicate calculus emphasizing proof theory rather than model theory. Gives some programming exercises. LEC 335 Elements of Geometry (4) (Sp) Prerequisites: MTH301, MTH309 Euclidean and non-Euclidean geometries. Study of the Hilbert postulates and various models, with emphasis on Euclidean and Lobachevskian geometries. LEC/LAB 336 Projective Geometry (4) Prerequisite: MTH241 or permission of instructor Projective geometry is both a generalization and a simplification of familiar Euclidean geometry, omitting concepts of distance and angle. The small set of axioms has an important duality property. There are several famous theorems relating figures in the plane. Three-D geometry and specialization to Euclidean and other geometries may be considered, as time permits. Requires no previous geometry. LEC 337 Introduction to Scientific Computing (4) (F; Sp) Prerequisite: MTH141 For students in all scientific disciplines. Introduces the fundamental numerical techniques used in high-performance scientific computing, including sorting, numerical integration, root finding for nonlinear systems, elementary linear algebra, and basic ordinary differential equations. Emphasizes an experimental approach to scientific computing. Students learn the basics of UNIX, write and debug programs in FORTRAN, and use computational and visualization tools in Matlab. Cross-listed as CSE337. LEC/LAB 343 Codes (3) Prerequisite: MTH309 Study of the characteristics and mathematical foundations of several codes widely used in information handling for data compression, error detection, error correction and other special purposes. The codes studied include binary, comma-free, cryptographic, cyclic, Hamming, and Huffman. LEC 353 Introduction to Combinatorics I (3) (F) Prerequisite: MTH241 Permutations, combinations, and other problems of selecting and arranging objects subject to various restrictions; generating functions; recurrence relations; inclusion-exclusion theorem. LEC 354 Introduction to Combinatorics II (3) (Sp) Prerequisite: MTH241 Theory of graphs: Eulerian and Hamiltonian circuits; trees; planarity; colorability; directed graphs and tournaments; isomorphism; adjacency matrix; applications to problems in communication, scheduling, and traffic flow. LEC 411 Probability Theory (4) (F) Prerequisites: MTH141-142 or equivalent A first course in probability. Introduces the basic concepts of probability theory and addresses many concrete problems. A list of basic concepts includes axioms of probability, conditional probability, independence, random variables (continuous and discrete), distribution functions, expectation, variance, joint distribution functions, limit theorems. LEC/REC 412 Introduction to Statistical Inference (4) (Sp) Prerequisites: MTH141 or equivalent and MTH411 or STA401 or permission of instructor Topics include: review of probability, conditional probability, Bayes' Theorem; random variables and distributions; expectation and properties; covariance, correlation, and conditional expectation; special distributions; Central Limit Theorem and applications; estimations, including Bayes; estimators, maximum likelihood estimators, and their properties. Includes use of sufficient statistics to 'improve' estimators, distribution of estimators, unbiasedness, hypothesis testing, linear statistical models, and statistical inference from the Bayesian point of view. REC 413 Introduction to Mathematical Logic I (3) (F) Prerequisite: MTH313 or permission of instructor Informal and formal development of propositional calculus; predicate calculus and predicate calculus with equality; completeness theorem and some consequences. LEC 414 Introduction to Mathematical Logic II (3) (Sp) Prerequisite: MTH314 or MTH413 Godel's incompleteness theorem; decidability and recursiveness; consistency problems. LEC 417 Survey of Multivariable Calculus (4) (F; Sp) Prerequisite: MTH241 For math majors in Concentration C, and majors of science and engineering. Surveys functions of several variables; differentiation, composite, and implicit functions; critical points; line integrals; Green's theorem. Vector field theory; gradient, divergence, and curl; integral theorems. Introduces functions of a complex variable; curves and regions in the complex plane; analytic functions, Cauchy-Riemann equations, Cauchy integral formula. Applications. LEC/LAB 418 Survey of Partial Differential Equations (4) (F; Sp) Prerequisite: MTH306 For math majors in Concentration C, and majors of science and engineering. Surveys elementary differential equations of physics; separation of variables and superposition of solutions; orthogonal functions and Fourier series. Introduces boundary value problems, Fourier and Laplace transforms. LEC/LAB 419 Introduction to Algebra I (4) (F; Sp) Prerequisite: MTH309; MTH301 recommended Note: Students who have not completed MTH309, but who have had an equivalent course, need to obtain a waiver from the director of undergraduate studies. Emphasizes theorems and proofs. Groups, cosets, group-homomorphisms. Rings, modules, and morphisms between them. Ideals in a commutative ring (with 1). The residue-class ring R/a. Minimal and maximal ideals. LEC/REC 420 Introduction to Algebra II (4) (Sp) Prerequisite: MTH419 Continuation of MTH419. Quotient field of an integral domain; fields; vector spaces; field extensions; finite fields; modules; irreducible modules; Wedderburn-Artin structure theorems. LEC/REC 425 Introduction to Complex Variables I (3) Prerequisite: MTH417 or MTH431 or permission of instructor For students of physics, electrical and other areas of engineering, and mathematics. Analyticity; calculus over the complex numbers. Cauchy theorems, residues, singularities, conformal mapping. Weierstrass convergence theorem; analytic continuation. LEC 426 Introduction to Complex Variables II (3) Prerequisite: MTH425 Continuation of MTH425. Weierstrass and Mittag-Leffler theorems, harmonic functions, conformal mapping and Green's function, analytic equivalence, and Riemann's mapping theorem. Montel's theorem, external mappings. LEC 427 Introduction to Topology I (3) (F) Prerequisite: MTH431 Abstract topological spaces, bases, convergence, filters, and nets; separation axioms, continuity, and homeomorphisms; connectedness, separability, compactness. LEC 428 Introduction to Topology II (3) (Sp) Prerequisite: MTH427 Continuation of MTH427. Product and quotient topologies; compactification; complete semi-metric spaces; metrization; topological algebra. Applies results to such fields as differential equations, numerical analysis, probability theory. LEC 429 Introduction to the Theory of Numbers I (3) (F) Prerequisite: MTH419 The Euclidean algorithm and unique factorization; arithmetical functions; congruences, reduced residue systems; primitive roots; certain diophantine equations. LEC 430 Introduction to the Theory of Numbers II (3) (Sp) Prerequisite: MTH429 Continuation of MTH429. Irrational numbers; continued fractions from a geometric viewpoint; best rational approximations to real numbers; the Fermat-Pell equation; quadratic fields and integers. Applications to diophantine equations. LEC 431 Introduction to Real Variables I (4) (F) Prerequisite: MTH301 Students who have not completed MTH301, but who have had an equivalent course, need to obtain a waiver from the director of undergraduate studies. Comprehensive and rigorous course in the study of real valued functions of one real variable. Topics include sequences of numbers, limits and the Cauchy criterion, continuous functions, differentiation, inverse function theorem, Riemann integration, sequences and series, uniform convergence. A prerequisite for most advanced courses in analysis. LEC/LAB 432 Introduction to Real Variables II (4) (Sp) Prerequisite: MTH431 Rigorous course in the study of analysis in dimensions greater than one. Three basic theorems: the inverse function theorem, the implicit function theorem, and the change of variables theorem in multiple integrals are among the subjects studied in detail. Topics include continuously differentiable functions, the chain rule, inverse and implicit function theorems, Riemann integration, partitions of unity, change of variables theorem. LEC/REC 434 Basic Measure Theory (3) Prerequisite: MTH431 or permission of instructor The real numbers, the extended numbers, sequences, limit superior and limit inferior, topology for the real numbers and continuity of functions. The Lebesgue outer measure, measurable sets and Lebesgue measure, nonmeasurable sets, measurable functions. Egoroff's Theorem and Lusin's Theorem. The Riemann integral, the Lebesgue integral and the convergence theorems. Differentiation of functions of bounded variation, absolute continuity. The Lp spaces. LEC/LAB 437 Introduction to Numerical Analysis I (4) (F; Sp) Prerequisite: CSE113, MTH241, MTH306, MTH309, or permission of instructor Lagrangian interpolation; quadrature formulae; difference equations; numerical solution of ordinary differential equations; predictor-corrector and Runge-Kutta methods. LEC/LAB 438 Introduction to Numerical Analysis II (4) (F; Sp) Prerequisite: MTH437 Solution of linear and nonlinear systems of equations; calculation of eigenvalues and eigenvectors; introduces the numerical solution of boundary-value problems for both ordinary and partial differential equations. LEC/LAB 443 Fundamentals of Applied Mathematics I (4) Prerequisite: MTH306 Mathematical formulation and analysis of models for phenomena in the natural sciences. Includes derivation of relevant differential equations from conservation laws and constitutive relations. Potential topics include diffusion, stationary solutions, traveling waves, linear stability analysis, scaling and dimensional analysis, perturbation methods, variational and phase-space methods, kinematics, and laws of motion for continuous media. Examples from areas might include, but are not confined to, biology, fluid dynamics, elasticity, chemistry, astrophysics, geophysics. LEC 444 Fundamentals of Applied Mathematics II (4) Prerequisite: MTH443 Continues topics described in MTH443. LEC 445 Ordinary Differential Equations (3) Prerequisite: MTH431 or permission of instructor For students with a strong mathematics background. Existence and uniqueness of solutions; continuation of solutions; dependence on initial conditions and parameters; linear systems of equations with constant and variable coefficients; autonomous systems, phase space, and stability. LEC 449 Introduction to Partial Differential Equations (3) Prerequisite: permission of instructor For students with a strong mathematics background. Students must know the material of both MTH431 and MTH306. Classical linear equations of mathematical physics, well-posed problems, qualitative properties of solutions. Techniques for solving problems. LEC 455 Mathematical Modeling (3) Prerequisites: MTH306, MTH309 Introduces the use of mathematical modeling in applied mathematics using a case study approach. Population ecology; chemical kinetics; traffic dynamics. LEC 457 Problem Solving Seminar (3) Prerequisites: MTH306, MTH411 or STA401, and some experience with scientific programming; minimum grade of "B" in these courses. Open discussion and solving of a series of quantitatively based problems involving both individual and student team efforts. Central to the active and cooperative learning experience is the communication of results in the form of carefully written technical reports and oral presentations. Analytic, geometric, and numerical problem solving techniques may all be used. LEC 458 Mathematical Finance (3) Prerequisite: MTH241, MTH309, MTH306 Introduces the mathematical theory and computation of modern financial products used in the banking and corporate world. Derives and analyzes mathematical models for the valuation of derivative products. LEC 460 Theory of Games (3) Prerequisite: MTH419, MTH431, or permission of instructor Finite, N-person, non-zero-sum, and infinite games. Two-person games with complete information. Incomplete information; mixed strategies; minimax theorem. LEC 465 Lectures on Geometry (3) Prerequisites: MTH309, permission of instructor Provides a broader understanding of differential geometry. Includes a comprehensive introduction to the theory of curves and surfaces in space. Moves toward the goal of viewing surfaces as special concrete examples of differentiable manifolds. This goal is reached by studying surfaces using tools that are basic to the study of manifolds. Topics include curves in 3-D space, differential forms, Frenet formulae, patch computations, curvature, isometries, intrinsic geometry of surfaces. Serves as an introduction to more advanced courses involving differentiable manifolds. LEC 461-464 and 466-469 Topics Courses (3) Each of these courses is a topics course that treats problems, methods, and recent developments pertaining to a specific area of mathematics indicated below. Each course can be taken more than once for credit. 461 Topics on Algebra (3) Prerequisite: MTH420 LEC 462 Topics on Analysis (3) Prerequisite: MTH432 LEC 463 Topics on Applied Mathematics (3) Prerequisite: permission of instructor LEC 464 Topics on Combinatorial Analysis (3) Prerequisite: permission of instructor LEC 466 Topics on Logic and Set Theory (3) Prerequisite: permission of instructor LEC 467 Topics on Number Theory (3) Prerequisite: permission of instructor LEC 468 Topics on Numerical Analysis (3) Prerequisite: permission of instructor LEC 469 Topics on Topology (3) Prerequisite: permission of instructor LEC 497 Honors Thesis in Mathematics (4) (F; Sp) Prerequisite: math major seeking honors degree in mathematics Open only to math majors intending to seek an honors degree in mathematics. For information, consult the director of undergraduate studies in the Department of Mathematics. TUT 498 Internship in Mathematics (1-4) (F; Sp) Prerequisites: accepted math major; junior/senior standing with a minimum of 24 credits in mathematics; permission of director of undergraduate studies Students get field experience in mathematical employment, in business, industry, or education, working under the joint supervision of an off-campus supervisor and a university faculty member, usually the director of undergraduate studies. May be taken once only. TUT 499 Independent Study (1-4) (F; Sp) Individual study arranged between student and faculty member in an area of mathematics of particular interest to the student. TUT Checklist for Math Majors Complete MTH141, 142, 241 with a minimum GPA of 2.5 Apply to the department while enrolled in MTH241, or any time after that. Applicants should bring a copy of their current UB DARS report directly to the Department of Mathematics. If you choose to be in the Basic Curriculum Program, no further approval is necessary. If you intend to major in mathematics with one of the concentrations listed below, you must obtain approval from the director of undergraduate studies no later than the end of the semester in which you are admitted. If you do not receive approval and do not meet with the director of undergraduate studies to review your program, you will be placed in the basic curriculum and your progress will be monitored according to those requirements. Concentration C: Computing and Applied Mathematics Concentration GS/ED: General Study in Mathematics and Education (Also apply for the Education Minor) Concentration GS: General Study in Mathematics Concentration GS/AM: General Study in Applied Mathematics Concentration BSc: General Study in Mathematics (B.S. degree) Concentration BSc/AM: General Study in Applied Mathematics (B.S. degree) Program M/E: Joint Major in Mathematics/Economics (B.A. degree) (Also apply to economics department) Program M/P: Joint Major in Mathematical Physics (B.S. degree) (Also apply to physics department) Program Leading to Combined B.A./M.A. Degree Schedule an appointment with the director of undergraduate studies at least once a year to review your progress toward a degree. If you plan to attend graduate school, you should discuss your plans with the director of undergraduate studies in spring of your junior year, and take the GREs by December of your senior year. In fall of your final year, talk to career development office regarding job interviews, résumés, etc. File for degree with the Office of Records and Registration one semester before your intended graduation date (check the deadline dates in the class schedule). Mathematics - B.S. Concentration BSc: General Study In Mathematics This concentration provides a basic theoretical course of study for mathematics majors intending graduate study in mathematics. Admission to this concentration is by departmental approval only. See the director of undergraduate studies regarding approval. Required Courses MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH301 Basic Analysis and Proofs MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH419 Introduction to Algebra I MTH420 Introduction to Algebra II MTH431 Introduction to Real Variables I MTH432 Introduction to Real Variables II Three 300/400-level mathematics courses (not MTH417) Four 300/400-level courses in mathematics or computer science (not MTH417) See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First-Third Years Follow first three years of concentration GS Fourth Year Three 300/400-level mathematics courses (not MTH417) Four 300/400-level courses in mathematics or computer science (not MTH417) Note: All seven electives do not necessarily need to be taken in the senior year. Summary Total required credit hours - 64-68 (seventeen courses in math and related areas) Mathematics - B.S. Concentration BSc/AM: General Study In Applied Mathematics This concentration provides a course of study for mathematics majors intending to pursue graduate study in applied mathematics. Admission to this concentration is by departmental approval only. See the director of undergraduate studies regarding approval. Required Courses CSE115 Introduction to Computer Science for Majors I CSE116 Introduction to Computer Science for Majors II MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH301 Basic Analysis and Proofs MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH310 Applications of Linear Algebra MTH418 Survey of Partial Differential Equations or MTH445 Ordinary Differential Equations or MTH419 Introduction to Algebra I MTH431 Introduction to Real Variables I MTH432 Introduction to Real Variables II MTH449 Introduction to Partial Differential Equations Two 300/400-level mathematics courses (not MTH417) Four 300/400-level courses in mathematics or computer science (not MTH417) PHY107 General Physics I PHY108 General Physics II See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First-Third Years Follow first three years of concentration GS/AM Fourth Year Two 300/400-level mathematics courses (not MTH417) Four 300/400-level courses in mathematics or computer science (not MTH417) Note: all six electives do not necessarily need to be taken in the senior year. Summary Total required credit hours in concentration BSc/AM - 77-83 (twenty-three courses in math and related areas) Mathematics - B.A. Basic Curriculum in Mathematics This is the basic liberal arts major program in mathematics, and allows for freedom in course choice to the students. A total of nine mathematics (MTH) courses are required: four core courses (MTH141, MTH142, MTH241, MTH309) generally completed in the first two years, and five electives. Several concentrations requiring additional coursework are available for students with specific career goals. Acceptance Criteria Minimum of 2.5 GPA in MTH141, 142 and 241 (or transfer equivalents) Required Courses MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH309 Introduction to Linear Algebra One of the following: MTH306 Introduction to Differential Equations, MTH337 Introduction to Scientific Computing, MTH437 Introduction to Numerical Analysis I, or other computer applications course approved by director of undergraduate studies in mathematics One of the following: MTH301 Basic Analysis and Proofs, MTH313 Elements of Set Theory, MTH335 Elements of Geometry, MTH419 Introduction to Algebra I, MTH431 Introduction to Real Variables I, or other proofs course approved by director of undergraduate studies in mathematics Three 300/400-level mathematics courses See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First Year Fall-MTH141 Spring-MTH142 Second Year Fall-MTH241 Spring-MTH309 Third Year Fall-One of the following: MTH306, MTH337, MTH437, or other computer applications course approved by director of undergraduate studies in mathematics Spring-One of the following: MTH301, MTH313, MTH335, MTH419, MTH431, or other mathematical proofs course approved by director of undergraduate studies in mathematics (Note: selections above must be made in consultation with director of undergraduate studies in mathematics.) Fourth Year Fall and Spring-Three 300/400 level-mathematics courses Each elective must be pre-approved by director of undergraduate studies in mathematics Summary Total required credit hours in basic curriculum - 33-36 (nine courses in mathematics) Mathematics - B.A. Concentration C: Computing and Applied Mathematics This concentration is designed to serve those students interested in careers as applied mathematicians or scientific applications programmers. The courses in this concentration are like the calculus and computing courses, though more difficult. A student who can handle MTH141, 142, 241, and CSE115, 116 should be able to handle concentration C. Required Courses CSE115 Introduction to Computer Science for Majors I CSE116 Introduction to Computer Science for Majors II CSE241 Digital Systems CSE250 Algorithms and Data Structures MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH417 Survey of Multivariable Calculus and MTH418 Survey of Partial Differential Equation or MTH431 Introduction to Real Variables I and MTH432 Introduction to Real Variables II* MTH437 Introduction to Numerical Analysis I MTH438 Introduction to Numerical Analysis II Two 300/400-level mathematics courses Two 300/400-level courses in mathematics or computer science See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First Year Fall-MTH141, CSE115 Spring-MTH142, CSE116 Second Year Fall-MTH241, CSE241 Spring-MTH306, CSE250 Third Year Fall-MTH309, MTH417 or MTH431 Spring-MTH418 or MTH432* Fourth Year Fall-MTH437 Spring-MTH438 Fall or Spring-Two 300/400-level mathematics courses, two 300/400-level courses in mathematics or computer science *MTH301 is a prerequisite for MTH431. Students must take one complete sequence: MTH417-418 or MTH431-432. Students intending to go to graduate school in applied mathematics should take MTH301-431-432 instead of MTH417-418. MTH301 would then count as a technical elective. Approved Technical Electives Recommended Any other 300/400-level MTH course would also be acceptable. MTH301 may be taken as an elective; it is the first abstract theoretical course with proofs. Note that MTH431-432 and MTH419-420 are designed for students who want intensive preparation in analysis and modern algebra, and are not good choices to just fill out their schedule. MTH431-432 may be taken as electives (in addition to MTH417 or MTH418) or as requirements (in place of MTH417 and MTH418). Approved technical electives outside the mathematics department: CSE305, CSE351, 400-level CSE courses Note: Both CSE480 Computer Graphics and MTH463 Topics in Applied Mathematics may be taken as technical electives, one in and one outside the department. Summary Total required credit hours in concentration C - 64-68 (seventeen courses in math and related areas) Mathematics - B.A. Concentration GS: General Study in Mathematics This concentration describes a basic theoretical course of study for mathematics majors intending to pursue graduate study in mathematics, or intending careers in such fields as actuarial science, financial analysis, or cryptography. Admission to this concentration is by departmental approval only. See the director of undergraduate studies regarding approval. Advising Notes Concentration GS has the fewest courses of any of the math programs, but many courses are quite difficult; MTH301, MTH431-432, and MTH419-420 are abstract theoretical courses emphasizing proofs. A student must do well in MTH301 to enter this program. Students planning to go to graduate school should meet with the director of undergraduate studies in mathematics in the fall semester of their junior year. They should plan to take the GREs in either spring of the junior year or fall of the senior year. It is strongly advised that students in concentration GS take MTH425, MTH427-428, and MTH465 as part of this program. Required Courses MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH301 Basic Analysis and Proofs MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH419 Introduction to Algebra I MTH420 Introduction to Algebra II MTH431 Introduction to Real Variables I MTH432 Introduction to Real Variables II One 300/400-level mathematics course (not MTH417) Two 300/400-level courses in mathematics or computer science (not MTH417) See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First Year Fall-MTH141 Spring-MTH142 Second Year Fall-MTH241, MTH309 Spring-MTH301, MTH306 Third Year Fall-MTH419, MTH431 Spring-MTH420, MTH432 Fourth Year Fall or Spring-One 300/400-level mathematics course (not MTH417), two 300/400-level courses in mathematics or computer science (not MTH417) Summary Total required credit hours in concentration GS - 49-52 (thirteen courses in math and related areas) Mathematics - B.A. Concentration GS/Am: General Study in Applied Mathematics This concentration describes a course of study for mathematics majors intending to pursue graduate study in applied mathematics. Admission to this concentration is by departmental approval only. See the director of undergraduate studies regarding approval. Advising Notes MTH301-431-432 and MTH419 are abstract theoretical courses emphasizing proofs. A student must do well in MTH301 to enter this program. Students planning to go to graduate school should meet with the director of undergraduate studies in mathematics in the fall semester of their junior year. They should plan to take the GREs in either spring of the junior year, or fall of the senior year. Required Courses CSE115 Introduction to Computer Science for Majors I CSE116 Introduction to Computer Science for Majors II MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH301 Basic Analysis and Proofs MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH310 Applications of Linear Algebra MTH418 Survey of Partial Differential Equations or MTH445 Ordinary Differential Equations or MTH449 Introduction to Partial Differential Equations MTH419 Introduction to Algebra I MTH431 Introduction to Real Variables I MTH432 Introduction to Real Variables II Two 300/400-level courses in mathematics or computer science (not MTH417) PHY107 General Physics I PHY108 General Physics II See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First Year Fall-CSE115, MTH141, PHY107 Spring-CSE116, MTH142, PHY108 Second Year Fall-MTH241, MTH309 Spring-MTH310, MTH301, MTH306 Third Year Fall-MTH431, MTH419 Spring-MTH432, MTH418 or MTH445 or MTH449 Fourth Year Fall or Spring-Two 300/400-level courses in mathematics or computer science (not MTH417) Summary Total required credit hours - 65-67 (seventeen courses in math and related areas) Mathematics-Economics - B.A. Program M/E: Joint Major in Mathematics/Economics This is a program for students intending graduate study in economics. Acceptance into this program requires a minimum GPA of 2.5 in both the mathematics and economics courses during the first year. Separate applications must be submitted to both the Department of Mathematics and the Department of Economics. Admission to this program is by departmental approval only. See the director of undergraduate studies regarding approval. Advising Notes A student must be able to handle MTH301 to enter this program. Students should consult the advisor in each department concerning senior-level courses. Exceptions in the curriculum may be allowed through consultation with the appropriate department. Interested students should contact the departments upon application for up-to-date information on possible changes. Required Courses ECO405 Microeconomic Theory ECO407 Macroeconomic Theory or ECO337 Honors Macroeconomic Theory MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH301 Basic Analysis and Proofs MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH411 Probability Theory MTH412 Introduction to Statistical Inference MTH419 Introduction to Algebra I MTH431 Introduction to Real Variables I One 300/400-level mathematics course (not MTH417) Two 300/400-level courses in economics (not ECO480 or 481) See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First Year Fall-MTH141 Spring-MTH142 Second Year Fall-ECO407 or ECO337, MTH241 Spring-ECO405, MTH301, MTH306, MTH309 Third Year Fall-MTH431, MTH411 Spring-MTH419, MTH412 Fourth Year Fall or Spring-One 300/400-level mathematics course (not MTH417), two 300/400-level courses in economics (not ECO480 or 481) Summary Total required credit hours - 58-61 (fifteen courses in math and economics) Mathematical Physics - B.S. Acceptance Criteria Minimum GPA of 2.5 in MTH141-142, MTH241, and PHY107-108/158 Separate applications must be submitted to both the Department of Mathematics and the Department of Physics. Admission to this program is by departmental approval only. See the director of undergraduate studies regarding approval. Advising Notes Students should consult with the advisor in each department regarding approved electives. This is a joint program. A student who follows this program but does not complete it, will have difficulty completing either a math major or a physics major without substantial additional coursework. Required Courses MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH417 Survey of Multivariable Calculus MTH418 Survey of Partial Differential Equations MTH419 Introduction to Algebra I MTH424 Fourier Series MTH425 Introduction to Complex Variables I One 300/400-level MTH elective PHY107 General Physics I or PHY117 Honors Physics I PHY108 General Physics II or PHY118 Honors Physics II PHY158 General Physics II Lab PHY207 General Physics III or PHY217 Honors Physics III PHY207 General Physics III Lab PHY208 General Physics IV PHY301 Intermediate Mechanics I PHY401 Modern Physics I PHY403 Electricity and Magnetism I PHY405 Thermal and Statistical Physics I PHY408 Advanced Laboratory One PHY elective (one of the following: PHY302 Intermediate Mechanics II, PHY402 Modern Physics II, PHY404 Electricity and Magnetism II, or PHY406 Thermal and Statistical Physics II) See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First Year Fall-MTH141 Spring-PHY107 or PHY117, MTH142 Second Year Fall-PHY108 or PHY118, PHY158, MTH241, MTH309 Spring-PHY207 or PHY217, PHY207, PHY208, MTH306 Third Year Fall-PHY301, PHY401, MTH417 Spring-One PHY elective (one of the following: PHY302, PHY402, PHY404, PHY406), MTH418 Fourth Year Fall-MTH419, MTH425, PHY403, PHY405 Spring-PHY408, MTH424, one 300/400-level MTH elective Summary Total required credit hours in mathematics and physics - 78 General education courses and electives - 42 Total required credit hours - 120 Mathematics - B.A. Concentration GS/ED: General Study in Mathematics and Education This concentration is designed for the student whose career goal is to attain a master's degree for professional certification in adolescent mathematics education. It is intended to be coupled with a minor in teacher education. Students interested in this concentration should obtain advisement from the director of undergraduate studies in mathematics, 233 Mathematics Building, and from the Teacher Education Institute (TEI), 379 Baldy Hall. Admission to the major must be sought from the Department of Mathematics, usually in the student's second year. Admission to the minor (after completion of certain prerequisite courses) must be sought separately through TEI in the student's third year. For advice on prerequisites for required courses in the minor and selection of general education courses fulfilling the State Education Requirement (SED) for prospective teachers, students should consult with TEI as early as their freshman year. Completion of the major concentration together with the education minor provides advanced status toward initial New York State teacher certification, accomplished through one year of subsequent coursework at the graduate level through the Graduate School of Education. It will then be possible to complete, within the state-mandated three years, the master's degree required for a professional teaching certificate, provided all NYS requirements have been successfully completed. Advising Notes The courses in this Concentration are more theoretical than those in Concentration C; MTH301, MTH419, and MTH431 are difficult. A student must be able to handle MTH301 in order to enter this concentration. A minimum GPA of 3.0 overall is required for admission to the minor in teacher education. Warning: In order to graduate with a degree in mathematics in concentration GS/ED, a student must be accepted into and complete the teacher education minor through TEI prior to graduation. The teacher education program has a limited number of openings; admission is based in part on interviews and can be very competitive in some years. Students who complete concentration GS/ED math requirements but do not gain admission to the teacher education minor will have to change to the basic curriculum or to another concentration in order to graduate. It is recommended that students interested in this concentration contact the department upon application for up-to-date information on possible changes in requirements. Required Courses CSE113 Introduction to Computer Science I or CSE115 Introduction to Computer Science for Majors I CSE114 Introduction to Computer Science II or CSE116 Introduction to Computer Science for Majors II MTH141 College Calculus I MTH142 College Calculus II MTH/CSE191 Introduction to Discrete Mathematics MTH241 College Calculus III MTH301 Basic Analysis and Proofs MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH335 Elements of Geometry MTH411 Probability Theory MTH419 Introduction to Algebra I MTH431 Introduction to Real Variables I LAI415 Introduction to Education CEP400 Educational Psychology ELP405 Social Foundations in Education LAI414 Language, Cognition & Writing LAI418 Instructional Strategies One 300/400-level mathematics elective (not MTH417) One 300/400-level elective from Educational Leadership and Policy or Counseling and Educational Psychology or one education-related College of Arts and Sciences course See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First Year Fall-MTH141, CSE113 or CSE115 Spring-MTH142, CSE114 or CSE116 Second Year Fall-MTH241, MTH/CSE191 Spring-MTH301, MTH306, LAI415 Third Year Fall-MTH309, MTH431 Spring-MTH335, CEP400, ELP405 Fourth Year Fall-MTH411, MTH419, LAI414, LAI418 Spring-One 300/400-level mathematics elective (not MTH417) One 300/400-level elective from Educational Leadership and Policy or Counseling, School, and Educational Psychology or one education-related College of Arts and Sciences course Summary Teacher education minor - 18 cr Total required credit hours in computer science - 8 Total required credit hours in mathematics - 47-48 (fourteen courses in math and related areas) *TEI is located in the Graduate School of Education (379 Baldy Hall). TEI administers and coordinates the NYS Education Department approved teacher education programs. Mathematics - B.A./M.A. This program is designed for students who demonstrate in their first two years of mathematical study a high level of competence and motivation. Upon admission to the B.A./M.A. program, students follow an integrated course of study leading to a B.A./M.A. degree. Admission to this program is by departmental approval only and requires a minimum GPA of 3.0 in mathematics courses (calculus, differential equations, linear algebra) as well as letters of recommendation. Required Courses MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH301 Basic Analysis and Proofs MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra MTH519 Introduction to Algebra I MTH520 Introduction to Algebra II MTH531 Introduction to Real Variables I MTH532 Introduction to Real Variables II Three 300/400-level courses in mathematics or computer science. At least one of these must be a mathematics course other than MTH417. Electives need approval by the director of undergraduate studies. Six graduate-level courses, including at least 12 credits in mathematics. Included must be at least one year-long sequence in mathematics at the 500 level or above (other than 519-520 or 531-532). Electives need approval by the director of graduate studies. See Baccalaureate Degree Requirements (page 254) for general education and remaining university requirements. Recommended Sequence of Major Requirements First Year Fall-MTH141 Spring-MTH142 Second Year Fall-MTH241, MTH309 Spring-MTH301, MTH306 Third Year Fall and Spring-Three 300/400-level courses in mathematics or computer science. At least one of these must be a mathematics course other than MTH417. Electives need approval by director of undergraduate studies in mathematics. Fourth Year Fall-MTH519, MTH531 Spring-MTH520, MTH532 Fifth Year Fall and Spring-Six graduate-level math electives, including at least 12 credits in mathematics. Included must be at least one year-long sequence in mathematics at the 500 level or above (other than MTH 519-520 or MTH 531-532). Electives need approval by director of graduate studies. Project or thesis Summary Total required undergraduate-level credit hours - 33-36 Total required graduate-level credit hours for the math B.A./M.A. - 30 Project or Thesis Refer to the Graduate School's Policies and Procedures Manual for Master's Candidate Requirements Mathematics - Minor Acceptance Criteria Minimum GPA of 2.5 in MTH141-142 and 241 (or approved transfer equivalent) Required Courses MTH141 College Calculus I MTH142 College Calculus II MTH241 College Calculus III MTH306 Introduction to Differential Equations MTH309 Introductory Linear Algebra Two additional 300/400-level mathematics electives from within the Department of Mathematics Note: A minimum GPA of 2.0 is required in these courses for departmental recommendation for a minor in mathematics. Total required credit hours - 26-28 (seven courses from within the mathematics department) Questions and Comments about this site should be sent to:
Last updated: Thursday, 09-Dec-2004 15:21:19 EST
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