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MATH 312: Statistical Computing and Applications
3.00 - 4.00 Credits
Lehigh University
Use of statistical computing packages; exploratory data analysis; Monte Carlo methods; randomization and resampling, application and interpretation of a variety of statistical methods in real world problems. Prerequisite: Math 12 or 231. (MA)
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MATH 312 - Statistical Computing and Applications
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MATH 316: Complex Analysis spring
3.00 - 4.00 Credits
Lehigh University
Concept of analytic function from the points of view of the Cauchy-Riemann equations, power series, complex integration, and conformal mapping. Prerequisite: MATH 301. (MA)
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MATH 316 - Complex Analysis spring
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MATH 32: Honors Calculus II fall-spring
4.00 Credits
Lehigh University
Same topics as in MATH 22, but taught from a more thorough and rigorous point of view. Prerequisite: MATH 31. (MA)
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MATH 32 - Honors Calculus II fall-spring
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MATH 320: Ordinary Differential Equations spring
3.00 - 4.00 Credits
Lehigh University
The analytical and geometric theory of ordinary differential equations, including such topics as linear systems, systems in the complex plane, oscillation theory, stability theory, geometric theory of nonlinear systems, finite difference methods, general dynamical systems. Prerequisite: MATH 205, or both MATH 23, 33 and MATH 242. (MA)
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MATH 320 - Ordinary Differential Equations spring
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MATH 322: Methods of Applied Analysis I fall
3.00 Credits
Lehigh University
Fourier series, eigenfunction expansions, Sturm-Liouville problems, Fourier integrals and their application to partial differential equations; special functions. Emphasis is on a wide variety of formal applications rather than logical development. Prerequisite: MATH 205 or consent of the department chair. (MA)
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MATH 322 - Methods of Applied Analysis I fall
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MATH 323: Methods of Applied Analysis II spring
3.00 Credits
Lehigh University
Green's functions; integral equations; variational methods; asymptotic expansions, method of saddle points; calculus of vector fields, exterior differential calculus. Prerequisite: MATH 322. (MA)
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MATH 323 - Methods of Applied Analysis II spring
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MATH 327: Groups and Rings fall
3.00 - 4.00 Credits
Lehigh University
An intensive study of the concepts of group theory including the Sylow theorems, and of ring theory including unique factorization domains and polynomial rings. Prerequisite: MATH 243 or consent of the department chair. (MA)
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MATH 327 - Groups and Rings fall
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MATH 329: Computability Theory spring
3.00 - 4.00 Credits
Lehigh University
Core development of classical computability theory: enumeration, index and recursion theorems, various models of computation and Church's Thesis, uncomputability results, introduction to reducibilities and their degrees (in particular, Turing degrees, or degrees of uncomputability), computable operators and their fixed points. (MA)
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MATH 329 - Computability Theory spring
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MATH 33: Honors Calculus III fall-spring
4.00 Credits
Lehigh University
Same topics as in MATH 23, but taught from a more thorough and rigorous point of view. Prerequisite: MATH 32. (MA)
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MATH 33 - Honors Calculus III fall-spring
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MATH 334: Mathematical Statistics spring
3.00 - 4.00 Credits
Lehigh University
Populations and random sampling; sampling distributions; theory of statistical estimation; criteria and methods of point and interval estimation; theory of testing statistical hypotheses. Prerequisite: MATH 231 or MATH 309. (MA)
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MATH 334 - Mathematical Statistics spring
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