• MATH 4991: Mathematical Research

  1.00 Credits

  Tennessee Technological University

  
  Prerequisite: C or better in MATH 1920 and consent of instructor. This course introduces students to the process of performing research. By reading papers the students will learn how to define open and significant problems, set up a research plan and, if applicable, define relevant experiments. Students will be required to give presentations on either their own or other people's research. These courses can be taken for credit more than once.
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• MATH 4992: Mathematical Research

  2.00 Credits

  Tennessee Technological University

  
  Prerequisite: C or better in MATH 1920 and consent of instructor. This course introduces students to the process of performing research. By reading papers the students will learn how to define open and significant problems, set up a research plan and, if applicable, define relevant experiments. Students will be required to give presentations on either their own or other people's research. These courses can be taken for credit more than once.
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• MATH 4993: Mathematical Research

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: C or better in MATH 1920 and consent of instructor. This course introduces students to the process of performing research. By reading papers the students will learn how to define open and significant problems, set up a research plan and, if applicable, define relevant experiments. Students will be required to give presentations on either their own or other people's research. These courses can be taken for credit more than once.
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• MATH 5010: Modern Algebra I

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: Grade of C or better in Math 2010 and Math 3400. Groups and subgroups including cyclic, abelian, finite; permutation groups, group homomorphisms, cosets and Lagrange's Theorem, normal subgroups and factor groups. Rings including integral domains, unique factoraization domains and Euclidean domains, ideals and factor rings, ring homomorphisms, fields and their extensions, geometric constructions.
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• MATH 5020: Modern Algebra II

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: Grade of C or better in Math 5010. Groups and subgroups including cyclic, abelian, finite; permutation groups, group homomorphisms, cosets and Lagrange's Theorem, normal subgroups and factor groups. Rings including integral domains, unique factoraization domains and Euclidean domains, ideals and factor rings, ring homomorphisms, fields and their extensions, geometric constructions.
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• MATH 5050: Number Theory

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: Consent of instructor. Properties of integers, division algorithms, prime numbers, diophantine equations, congruences. Students enrolled in the 5000-level course will be required to complete additional work as stated in the syllabus.
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• MATH 5060: 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 5110: 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. Students enrolled in the 5000-level course will be required to complete additional work as stated in the syllabus.
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• MATH 5120: 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. Students enrolled in the 5000-level course will be required to complete additional work as stated in the syllabus.
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• MATH 5210: Numerical Analysis I

  3.00 Credits

  Tennessee Technological University

  
  Prerequisite: MATH 4210 (5210): C or better in MATH 1920 (or consent of instructor for MATH 5210); 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, direct and iterative methods for linear systems. Students enrolled in the 5000-level course will be required to complete additional work as stated in the syllabus.
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