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MATH 8920: Master's Project Course
1.00 Credits
Clemson University
For students in the nonthesis option of the MS degree program in Mathematical Sciences. Successful completion includes a presentation of the master's project to the student's advisory committee and acceptance of the paper by the committee.
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MATH 8920 - Master's Project Course
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MATH 9000: Prof Devel in Math Sciences
1.00 Credits
Clemson University
Elements involved in pursuing a career as a professional mathematician with emphasis on broadening the student's mathematical experiences within a framework of improving professionalism in the areas of teaching and research skills. To be taken Pass/No Pass only.
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MATH 9000 - Prof Devel in Math Sciences
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MATH 9010: Probability Theory I
3.00 Credits
Clemson University
Axiomatic theory of probability; distribution functions; expectation; Cartesian product of infinitely many probability spaces, and the Kolmogorov consistency theorem; models of convergence; weak and strong laws of large numbers. Students are expected to have completed a graduate-level course in measure and integration and in introductory examinations before enrolling in this course.
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MATH 9010 - Probability Theory I
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MATH 9020: Probability Theory II
3.00 Credits
Clemson University
Continuation of MATH 9010; characteristic functions, infinitely divisible distributions, central limit theorems, laws of large numbers, conditioning, and limit properties of sums of dependent random variables, conditioning, martingales. Students are expected to have completed a course in measure-theoretic probability before enrolling in this course.
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MATH 9020 - Probability Theory II
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MATH 9040: Cmptr Exprmnts Uncrtnty Quant
3.00 Credits
Clemson University
Introduces classic and recent methodological developments in experimental design, statistical modeling, and uncertainty quantification of computer experiments. Response surface analysis, Gaussian process modeling, Bayesian optimization, space-filling designs, sensitivity analysis, and statistical calibration are covered. Students are expected to have completed a graduate-level course in linear regression before enrolling in this course.
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MATH 9040 - Cmptr Exprmnts Uncrtnty Quant
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MATH 9270: Functional Analysis
3.00 Credits
Clemson University
Linear operators on specific spaces, spectral theory, semigroups of operators and the Hille-Yosida theorem, applications of linear spaces and operators, convexity. Students are expected to have completed a graduate-level course in linear analysis before enrolling in this course.
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MATH 9270 - Functional Analysis
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MATH 9500: Commutative Algebra
3.00 Credits
Clemson University
This course covers the fundamentals of commutative algebra and its algebraic geometric aspect, providing background for further study in algebraic geometry and algebraic number theory. Students must have completed at least one semester of graduate abstract algebra to enroll in this course.
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MATH 9500 - Commutative Algebra
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MATH 9510: Algebraic Number Theory
3.00 Credits
Clemson University
Covers arithmetic of number fields and number rings. Covers prime decomposition, ideal class groups, unit groups of number fields and distribution of prime ideals in number fields. Provides an overview of completions absolute values and valuation theory. Students are expected to have completed a graduate-level course in abstract algebra before enrolling in this course.
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MATH 9510 - Algebraic Number Theory
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MATH 9520: Analytic Number Theory
3.00 Credits
Clemson University
The theory of Fourier analysis and complex analysis are essential to modern number theory. Course focuses on applications of this theory to number theory, such as the proof of the prime number theorem and the connection of complex L-series to the distribution of primes and to arithmetic geometry. Students are expected to have completed a graduate-level course in linear analysis before enrolling in this course.
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MATH 9520 - Analytic Number Theory
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MATH 9540: Advanced Combinatorics
3.00 Credits
Clemson University
Further study of combinatorics and related areas of discrete mathematics. Content is drawn from graph theory, enumerative combinatorics, algebraic combinatorics, posets, and combinatorial designs, as well as algorithmic aspects and applications. Content may vary from year to year. Students are expected to have completed a graduate course in graph theory or combinatorics. May be repeated for credit as many times as needed/wanted.
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MATH 9540 - Advanced Combinatorics
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