• MATH 4086: Analytic Number Theory

  3.00 Credits

  University of Memphis

  
  Partial summation, Euler-Maclaurin summation formula, basic arithmetic functions and their mean values; Dirichlet series, Euler products; Meilin function and prime number theorem; characters and primes in arithmetic progressions, basic sieve methods. PREREQUISITE: MATH 3221 with a minimum grade of C-. COREQUISITE: MATH 4361.
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• MATH 4120: Ordinary Differential Eqns

  3.00 Credits

  University of Memphis

  
  MATH 4120/6120 - Ordinary Differential Equations (3) Existence and uniqueness of solutions, phase plane analysis, continuous dependence on data, stability by Lyapunov's methods, matrix exponentials, periodic solutions, invariance principle, Poincaré-Bendixson theorem, applications. PREREQUISITE: A grade of C or better in both MATH 2120 and MATH 3242; or permission of instructor.
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• MATH 4151: History of Mathematics

  3.00 Credits

  University of Memphis

  
  Development of mathematics from earliest times to present; problem studies; parallel reading and class reports. PREREQUISITE: 21 hours in MATH courses including MATH 2110 with a minimum grade of C-and one of MATH 2702, COMP 2700.
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• MATH 4171: Special Problems in Math

  1.00 - 3.00 Credits

  University of Memphis

  
  Directed individual study in selected area of mathematics chosen in consultation with instructor. Repeatable for a maximum of 3 credit hours by permission of department chair. PREREQUISITE: Permission of instructor.
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• MATH 4242: Linear Algebra

  3.00 Credits

  University of Memphis

  
  Linear transformations, polynomials, determinants, direct-sum decompositions, diagonalizable operators, rational and Jordan forms, inner product spaces, the spectral theorem. PREREQUISITE: MATH 3242 with a minimum grade of C-.
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• MATH 4261: Abstract Algebra

  3.00 Credits

  University of Memphis

  
  Groups; homomorphisms; rings; integral domains; polynomials; fields. PREREQUISITE: MATH 2702 with a minimum grade of C-and MATH 3242 with a minimum grade of C-, or permission of instructor.
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• MATH 4350: Intro Real Analysis I

  3.00 Credits

  University of Memphis

  
  Real number system, functions and sequences, limits, continuity, differentiation; Riemann-Stieltjes integration, series of functions. PREREQUISITE: MATH 2110 with a minimum grade of C-, MATH 2702 with a minimum grade of C-and MATH 3242 with a minimum grade of C-.
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• MATH 4351: Intro Real Analysis II

  3.00 Credits

  University of Memphis

  
  Integration theory; Riemann and Lebesgue integrals; partial differentiation, implicit function theorem. PREREQUISITE: MATH 4350 with a minimum grade of C-, or permission of instructor.
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• MATH 4361: Complex Variables

  3.00 Credits

  University of Memphis

  
  Complex numbers; analytic functions; Cauchy-Riemann conditions; Taylor and Laurent series; integration. PREREQUISITE: MATH 2110 with a minimum grade of C-.
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• MATH 4391: Partial Diffrntl Equation I

  3.00 Credits

  University of Memphis

  
  Laplace transforms; Fourier series; introduction to partial differential equations. PREREQUISITE: MATH 2120.
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