• MATH 4050: Number Theory

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: C or better in MATH 3400 or consent of instructor. Properties of integers, division algorithms, prime numbers, diophantine equations, and congruences.
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• MATH 4060: Topics in Cryptography

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: C or better in MATH 2010 and C or better in either MATH 3400 or CSC 2700. Fundamental concepts of cryptography presented with mathematical background (including groups, fields, elements of number theory, probability and statistics). Special attention will be given to the RSA algorithm, Elliptic Curve Cryptography, the EIGamal public key cryptosystem, Diffie-Hellman key exchange and pseudo random number generators.
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• MATH 4110: Advanced Calculus I

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4110 (5110): C or better in MATH 3400 or consent of instructor; MATH 4120 (5120): C or better in MATH 4110 (5110). Rigorous treatment of functions of one and several variables, improper integrals, sequences, infinite series, uniform convergence, and applications. Students are expected to improve their ability to work in an abstract setting using precise definitions and formal proofs and to present their work in class.
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• MATH 4120: Advanced Calculus II

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4110 (5110): C or better in MATH 3400 or consent of instructor; MATH 4120 (5120): C or better in MATH 4110 (5110). Rigorous treatment of functions of one and several variables, improper integrals, sequences, infinite series, uniform convergence, and applications. Students are expected to improve their ability to work in an abstract setting using precise definitions and formal proofs and to present their work in class.
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• MATH 4210: Numerical Analysis I

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4210 (5210): C or better in MATH 1920; MATH 4220 (5220): C or better in MATH 2120 or consent of instructor. Iterative methods for nonlinear equations, computational error analysis, convergence of iterative techniques, interpolation, numerical differentiation and integration, approximate solutions of initial-value problems, boundary-value problems, and nonlinear systems, and direct and iterative methods for linear systems.
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• MATH 4220: Numerical Analysis II

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4210 (5210): C or better in MATH 1920; MATH 4220 (5220): C or better in MATH 2120 or consent of instructor. Iterative methods for nonlinear equations, computational error analysis, convergence of iterative techniques, interpolation, numerical differentiation and integration, approximate solutions of initial-value problems, boundary-value problems, and nonlinear systems, and direct and iterative methods for linear systems.
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• MATH 4250: Adv Ord Diff Equations I

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4250 (5250): C or better in MATH 2110 and MATH 2120; MATH 4260 (5260): C or better in MATH 4250 (5250). Systems of ordinary differential equations, matrix methods, approximate solutions, stability theory, basic theory of nonlinear equations and differential systems, trajectories, phase space stability, and construction of liapunov functions.
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• MATH 4260: Adv Ord Diff Equations II

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4250 (5250): C or better in MATH 2110 and MATH 2120; MATH 4260 (5260): C or better in MATH 4250 (5250). Systems of ordinary differential equations, matrix methods, approximate solutions, stability theory, basic theory of nonlinear equations and differential systems, trajectories, phase space stability, and construction of liapunov functions.
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• MATH 4310: Intro to Topology I

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4310 (5310): C or better in MATH 3400; MATH 4320 (5320): C or better in MATH 4310 (5310). Topological spaces, continuity, connectedness, compactness, separation axioms, function spaces, and fundamental groups.
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• MATH 4320: Intro to Topology II

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4310 (5310): C or better in MATH 3400; MATH 4320 (5320): C or better in MATH 4310 (5310). Topological spaces, continuity, connectedness, compactness, separation axioms, function spaces, and fundamental groups.
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