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MATH 8520: Abstract Algebra II
3.00 Credits
Clemson University
Continuation of MATH 8510 including selected topics from ring theory and field theory. Offered fall semester only.
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MATH 8530: Matrix Analysis
3.00 Credits
Clemson University
Topics in matrix analysis that support an applied curriculum: similarity and eigenvalues; Hermitian and normal matrices; canonical forms; norms; eigenvalue localizations; singular value decompositions; definite matrices. Students are expected to have completed either an undergraduate-level course in both linear algebra and advanced calculus, or to have completed an undergraduate-level course in mathematical analysis before enrolling in this course.
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MATH 8540: Theory of Graphs
3.00 Credits
Clemson University
Connectedness; path problems; trees; matching theorems; directed graphs; fundamental numbers of the theory of graphs; groups and graphs. Offered spring semester only.
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MATH 8550: Combinatorial Analysis
3.00 Credits
Clemson University
Combinations; permutations; permutations with restricted position; Polya's theorem; principle of inclusion and exclusion; partitions; recurrence relations; generating functions; Mobius inversion; enumeration techniques; Ramsey numbers; finite projective and affine geometries; Latin rectangles; orthogonal arrays; block designs; error detecting and error correcting codes. Offered fall semester only. Students are expected to have completed an undergraduate-level course in linear algebra before enrolling in this course.
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MATH 8560: Ther of Error-Correcting Codes
3.00 Credits
Clemson University
Topics include code constructions such as Hammig, cyclic, BCH, Reed-Solomon, Goppa, algebraic geometry, finite geometry, low-density parity check, convolutional and polynomial codes; code parameters and bounds; and decoding algorithms. Students are expected to have completed a graduate-level course in matrix analysis before enrolling in this course.
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MATH 8570: Cryptography
3.00 Credits
Clemson University
Classical and modern cryptography and their uses in modern communication systems are covered. Topics include entropy, Shannon's perfect secrecy theorem, Advanced Encryption Standard (AES), integer factorization, RSA cryptosystem, discrete logarithm problem, Diffie-Hellman key exchange, digital signatures, elliptic curve cryptosystems, hash functions and identification schemes. Students are expected to have completed undergraduate-level courses in linear algebra, theory of probability, and modern algebra; or a graduate-level course in abstract algebra before enrolling in this course.
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MATH 8580: Number Theory
3.00 Credits
Clemson University
Covers topics and techniques from modern number theory including unique factorization, elementary estimates on the distribution of prime numbers, congruences, Chinese remainder theorem, primitive roots, n-th powers modulo an integer, quadratic residues, quadratic reciprocity, quadratic characters, Gauss sums and finite fields. Students are expected to have completed a graduate-level matrix analysis course before enrolling in this course.
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MATH 8600: Intro to Scientific Computing
3.00 Credits
Clemson University
Floating point models, conditioning and numerical stability, numerical linear algebra, integration, systems of ordinary differential equations and zero finding; emphasis is on the use of existing scientific software. Students are expected to have completed undergraduate-level courses in computer programming language, ordinary differential equations, and linear algebra before enrolling in this course.
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MATH 8610: Advanced Numerical Analysis I
3.00 Credits
Clemson University
Consideration of topics in numerical linear algebra: eigenvalue problems, the singular value decomposition, iterative algorithms for solving linear systems, sensitivity of linear systems, and optimization algorithms. Students are expected to have completed undergraduate-level courses in linear algebra and numerical analysis; or a graduate-level course in scientific computing before enrolling in this course.
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MATH 8630: Digital Models I
3.00 Credits
Clemson University
Experimental mathematics; pseudostochastic processes; analytical and algebraic formulations of time-independent simulation; continuous-time simulation and discrete-time simulation; digital optimization; Fibonacci search; ravine search; gradient methods; current research in digital analysis. Offered fall semester only. Students are expected to have digital computer experience and to have completed undergraduate-level courses in linear algebra, advanced calculus, and computer programming language before enrolling in this course.
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