MATHEMATICS
Professors H.D. Junghenn, M.M. Gupta, E.A. Robinson, F.E. Baginski, D.H. Ullman, J. Przytycki, J. Bonin, V. Harizanov, Y. Rong, J.B. Conway (Chair)
Associate Professors M. Moses, W. Schmitt, L. Abrams
Assistant Professors I. Yi, K. Gurski, A. Shumakovitch
Bachelor of Arts with a major in mathematics—The following requirements must be fulfilled:
1. The general requirements stated under Columbian College of Arts and Sciences.
2. Prerequisite courses—Math 21 or 31, and Math 32 and 33. 3. Required courses in the major—a minimum of 27 additional credit hours of approved 100-level courses in mathematics, including Math 121, 124, 139, 140, and either Math 122 or 125.
Bachelor of Science with a major in applied mathematics—The following requirements must be fulfilled:
1. The general requirements stated under Columbian College of Arts and Sciences.
2. Prerequisite courses—Math 21 or 31, and Math 32 and 33. 3. Required courses in the major—a minimum of 27 additional credit hours of approved 100-level courses in mathematics, including Math 124, 139, 142, 143, and either Math 153 or 157. 4. Required courses in a related area—12 additional credit hours, to be selected in consultation with a departmental advisor, from a related area such as statistics, computer science, physics, engineering, chemistry, biology, economics, or applied science. At least 6 of these hours must be chosen from courses at the 100 level or higher.
Special Honors—To graduate with Special Honors, a student must meet the general requirements stated under University Regulations; maintain a grade-point average of at least 3.5 in mathematics courses; enroll in 3 credit hours of Math 195 in addition to the 27 credit hours of required courses in the major; and present an oral defense of a senior thesis prepared for Math 195.
Minor in mathematics—18 hours in mathematics courses, of which at least 12 are at the 100 level or higher, chosen in consultation with a departmental advisor.
With permission, graduate courses in the department may be taken for credit toward an undergraduate degree. See the Graduate Programs Bulletin for course listings.
Note: Math 21, 31, and 52 are related in their subject matter, and credit for only one of the three may be applied toward a degree. For courses that indicate the placement examination as prerequisite, see https://my.gwu.edu/mod/placement/.
| 3 |
College Algebra (3) |
Staff |
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Equations and inequalities, functions and graphs, polynomial and rational functions, exponential and logarithmic functions, systems of equations. |
| 7 |
Mathematics and Politics (3) |
Staff |
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A mathematical treatment of fair representation, voting systems, power, and conflict. The impossibility theorems of Balinsky and Young and of Arrow. The electoral college. The prisoner's dilemma. |
| 9–10 |
Mathematical Ideas I–II (3–3) |
Staff |
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Math 9: Elementary mathematical models of growth and decay, scaling, chaos, and fractals. Math 10: Elementary graph theory, scheduling, probability theory. |
| 20–21 |
Calculus with Precalculus I–II (3–3) |
Staff |
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An introduction to single-variable calculus (differentiation and integration of algebraic and trigonometric functions with applications), with the concepts and techniques of precalculus developed as needed. Prerequisite to Math 20: Math 3 or the placement examination or a score of 560 or above on the SAT subject test in mathematics; Math 20 is prerequisite to Math 21. |
| 31 |
Single-Variable Calculus I (3) |
Staff |
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Limits and continuity. Differentiation and integration of algebraic and trigonometric functions with applications. Prerequisite: the placement examination or a score of 720 or above on the SAT subject test in mathematics. |
| 32 |
Single-Variable Calculus II (3) |
Staff |
| |
The calculus of exponential and logarithmic functions. L'Hopital's rule. Techniques of integration. Infinite series and Taylor series. Polar coordinates. Prerequisite: Math 21 or 31. |
| 33 |
Multivariable Calculus (3) |
Staff |
| |
Partial derivatives and multiple integrals. Vector-valued functions. Topics in vector calculus, including line and surface integrals and the theorems of Gauss, Green, and Stokes. Prerequisite: Math 32. |
| 51 |
Finite Mathematics for the Social and Management Sciences (3) |
Staff |
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Systems of linear equations, matrix algebra, linear programming, probability theory, and mathematics of finance. Prerequisite: Math 3 or the placement examination or a score of 560 or above on the SAT subject test in mathematics. |
| 52 |
Calculus for the Social and Management Sciences (3) |
Staff |
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Differential and integral calculus of functions of one variable; applications to business and economics. Prerequisite: Math 3 or the placement examination or a score of 560 or above on the SAT subject test in mathematics. |
| 91 |
Introductory Special Topics (1 to 3) |
Staff |
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Admission by permission of instructor. May be repeated for credit. |
| 101 |
Introduction to Mathematical Logic (3) |
Harizanov, Moses |
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Symbolic logic as a precise formalization of deductive thought. Logical correctness of reasoning. Formal languages, interpretations, and truth. Propositional logic and first-order quantifier logic suited to deductions encountered in mathematics. Prerequisite: Math 32 or permission of instructor. |
| 102 |
Axiomatic Set Theory (3) |
Harizanov, Moses |
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Cantor's theory of sets. Russell's paradox. Axiomatization of set theory as a framework for a contradiction-free mathematics. Finite, countable, and uncountable sets; ordinal and cardinal numbers; the axiom of choice. Prerequisite: Math 32 or permission of instructor. |
| 103 |
Computability Theory (3) |
Harizanov, Moses |
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The unlimited register machine as a model of an idealized computer. Computable functions, Church's thesis. Effective enumerability. Unsolvability of the halting problem and other theoretical limitations on what computers can do. Prerequisite: Math 32 or permission of instructor. |
| 106 |
Introduction to Topology (3) |
Rong, Shumakovitch |
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Metric spaces: completeness, compactness, continuity. Topological spaces: continuity, bases, subbases, separation axioms, compactness, local compactness, connectedness, product and quotient spaces. Prerequisite: Math 33 and 124 or permission of instructor. |
| 113 |
Introduction to Combinatorics (3) |
Bonin, Ullman, Schmitt |
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Introduction to combinatorial enumeration. Basic counting techniques, inclusion–exclusion principle, recurrence relations, generating functions, pigeonhole principle, bijective correspondences, and applications to computer science, optimization, and coding theory. Prerequisite: Math 32. |
| 120 |
Elementary Number Theory (3) |
Bonin |
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Divisibility of integers, prime numbers, greatest common divisor, the Euclidean algorithm, congruence, the Chinese remainder theorem, number theoretic functions, M'bius inversion, Euler's phi function, and applications to cryptography and primality testing. Prerequisite: Math 31. |
| 121 |
Introduction to Abstract Algebra I (3) |
Abrams, Schmitt |
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Study of groups and associated concepts, including Lagrange's theorem, Cayley's theorem, the fundamental theorem of homomorphisms, and applications to counting. Prerequisite: Math 32 and 124 or permission of instructor. |
| 122 |
Introduction to Abstract Algebra II (3) |
Abrams, Schmitt |
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Study of rings, through maximal and prime ideals, and the study of fields, through Galois theory. Prerequisite: Math 121. |
| 124 |
Linear Algebra I (3) |
Robinson, Ullman |
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Linear equations, matrices, inverses, and determinants. Vector spaces, rank, eigenvalues, and diagonalization. Applications to geometry and ordinary differential equations. Prerequisite: Math 21 or 31, or 51 and 52, or permission of instructor. |
| 125 |
Linear Algebra II (3) |
Abrams, Yi |
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Theory of vector spaces, linear transformations, and matrices. Quadratic and bilinear forms. Characteristic polynomials and the Cayley–Hamilton theorem. Similarity and Jordan canonical form. Prerequisite: Math 124. |
| 132 |
Introduction to Graph Theory (3) |
Bonin, Ullman |
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Fundamental concepts, techniques, and results of graph theory, including applications to operations research, computer science, chemistry, and the social sciences. Topics include trees, connectivity, traversability, matchings, coverings, colorability, planarity, networks, and Polya enumeration. Prerequisite: Math 21 or 31. |
| 135 |
Projective Geometry (3) |
Bonin |
| |
Projective spaces, projectivities, conics, pairs and pencils of conics, finite planes, coordinates, collineation, Desarguesian planes. Prerequisite: Math 120 or 121 or permission of the instructor. |
| 139 |
Advanced Calculus I (3) |
Conway, Junghenn, Ullman |
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A rigorous study of differentiation, integration, and convergence. Topics include sequences and series, continuity and differentiability of real-valued functions of a real variable, the Riemann integral, sequences of functions, and power series. Prerequisite: Math 33 and 124 or permission of instructor. |
| 140 |
Advanced Calculus II (3) |
Conway, Junghenn, Ullman |
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Continuation of Math 139. Topics include: topology of Rn, derivatives of functions of several variables, inverse and implicit function theorems, multiple integrals, generalized Stokes's theorem. Prerequisite: Math 139 or permission of instructor. |
| 142 |
Ordinary Differential Equations (3) |
Gupta, Gurski |
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A first course in ordinary differential equations with an emphasis on mathematical modeling: solution curves, direction fields, existence and uniqueness, approximate solutions, first and second order linear equations, linear systems, phase portraits, and Laplace transforms. Prerequisite: Math 32 and 124 or permission of instructor. |
| 143 |
Partial Differential Equations (3) |
Baginski, Gurski |
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A first course in partial differential equations: Fourier series and separation of variables, vibrations of a string, Sturm–Liouville problems, series solutions, Bessel's equation, linear partial differential equations, wave and heat equations, separation of variables. Prerequisite: Math 33 and 124 or permission of instructor. |
| 148 |
Differential Geometry (3) |
Baginski, Robinson |
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Curves in space, regular surfaces, tensors, fundamental forms of a surface. Gauss–Bonnet theory, minimal surfaces. The geometry of the Gauss map. Prerequisite: Math 33 and 124 or permission of instructor. |
| 153 |
Introduction to Numerical Analysis (3) |
Baginski, Gupta |
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Accuracy and precision. Linear systems and matrices. Direct and iterative methods for solution of linear equations. Sparse matrices. Solution of nonlinear equations. Interpolation and approximate representation of functions, splines. Prerequisite: Math 32 and 124 and some knowledge of computer programming. |
| 157 |
Introduction to Complex Variables (3) |
Conway, Junghenn |
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Analytic functions and power series. Contour integration and the calculus of residues. Conformal mapping. Physical applications. Prerequisite: Math 33 and 124 or permission of instructor. |
| 170 |
Computational Complexity (3) |
Harizanov, Moses |
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Deterministic and nondeterministic Turing machines. Partial recursive functions and the Church–Turing thesis. Undecidable problems. Space and time complexity measures. Gap, speed-up, and union theorems. Decidable but intractable problems. The traveling salesman problem and other NP-complete problems. Prerequisite: Math 32 or permission of instructor. |
| 181 |
Seminar: Topics in Mathematics (3) |
Robinson and Staff |
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Past topics have included computational mathematics, fractals; network flows and combinatorial optimization; information theory and coding theory; dynamical systems; queuing theory. May be repeated for credit with permission. Prerequisite: Math 33 and 124 or permission of instructor. |
| 191 |
Special Topics (arr.) |
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Admission by permission of instructor. May be repeated for credit. |
| 195 |
Reading and Research (arr.) |
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Under the personal direction of an instructor. Limited to mathematics and applied mathematics majors with demonstrated capability. Prior approval of instructor required. May be repeated for credit. |
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